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MATHS 1 Marks Question

Squares and Square Roots · Gujarat Board (GSEB) STD 8 (GSEB - English Medium). 90 questions.

Questions · Page 2 of 2

1 Marks Question

Question 511 Mark
Without doing any calculation, find the number which are surely not perfect squares.
408
Answer
We know that the numbers end with $2,3,7$ or 8 , can never be a perfect square.
In a number 408, end digit is 8 , which is one of $2,3,7$ or 8 .
So, it never be a perfect square.
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Question 521 Mark
Without doing any calculation, find the number which are surely not perfect squares.
257
Answer
We know that the numbers end with $2,3,7$ or 8 , can never be a perfect square.
In a number 257, end digit is 7 , which is one of $2,3,7$ or 8 . So, it never be a perfect square.
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Question 531 Mark
Without doing any calculation, find the number which are surely not perfect squares.
153
Answer
We know that the numbers end with $2,3,7$ or 8 , can never be a perfect square.
In a number 153, end digit is 3 , which is one of 2, 3, 7 or 8 . So, it never be a perfect square.
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Question 561 Mark
Write a Pythagorean triplet whose one member is
14
Answer
Given number is 14.
On putting 2m = 14
$\Rightarrow \quad m=7$
So, $m^2-1=7^2-1=49-1=48$
and $m^2+1=7^2+1=49+1=50$
Hence, (14, 48, 50) is a Pythagorean triplet.
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Question 571 Mark
Write a Pythagorean triplet whose one member is
6
Answer
Given number is 6.
On putting 2m = 6
$\Rightarrow \quad m=\frac{6}{2}=3$
$\text { So, } m^2-1=3^2-1=9-1=8$
$\text { and } m^2+1=3^2+1=9+1=10$
Hence, (6, 8, 10) is a Pythagorean triplet.
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Question 621 Mark
Find the square of the following number
35
Answer
Given, number can be rewritten as $35=(30+5)$
On squaring both sides, we get
$\begin{aligned} 35^2 & =(30+5)^2=(30+5)(30+5) \\ & =30(30+5)+5(30+5) \\ & =900+150+150+25 \\ & =900+300+25=1225\end{aligned}$
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Question 631 Mark
Find the square of the following number
32
Answer
Given, number can be rewritten as 32 = (30 + 2)
On squaring both sides, we get
$\begin{aligned} 32^2 & =(30+2)^{2}=(30+2)(30+2) \\ & =30(30+2)+2(30+2) \\ & =900+60+60+4 \\ & =900+120+4=1024\end{aligned}$
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Question 641 Mark
Using the given pattern, find the missing numbers.
$1^2+2^2+2^2=3^2, \quad 2^2+3^2+6^2=7^2$,
$3^2+4^2+12^2=13^2, \quad 4^2+5^2+\_^2=21^2$,
$5^2+{ }\_^2+30^2=31^2, \quad 6^2+7^2+{ }\_^2=\_^2$
Answer
The missing numbers are as follows:
$ \begin{array}{l} 4^2+5^2+20^2=21^2, \quad 5^2+6^2+30^2=31^2 \\ 6^2+7^2+42^2=43^2 \end{array}$
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Question 651 Mark
Observe the following patterns and supply the missing numbers
$\begin{aligned} 11^2 & =121 \\ 101^2 & =10201 \\ 10101^2 & =102030201 \\ 1010101^2 & =\ldots . . . . . . . . .. . . .\\ .........&{ }^2=10203040504030201\end{aligned}$
Answer
According to the first three patterns, we see that given numbers are in odd digits. When we square the given number, we get the number in the odd position. Starting from 1 and consecutive increasing number upto the number of odd digits in the given number and then consecutive decreasing number upto 1 and all the even position number 0 exist.
(i) $1010101^2=1020304030201$
(ii) $101010101^2=10203040504030201$
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Question 661 Mark
The following numbers are obviously not perfect square. Give reason.
505050
Answer
The given number 505050 ends with 0, so it cannot be a perfect square due to odd number of zeroes.
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Question 671 Mark
The following numbers are obviously not perfect square. Give reason.
222000
Answer
The given number 222000 ends with 0, so it cannot be a perfect square due to odd number of zeroes.
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Question 681 Mark
The following numbers are obviously not perfect square. Give reason.
89722
Answer
The given number 89722 ends with 2, which is not of the end digit of 0, 1, 4, 5, 6 or 9, so it cannot be a perfect square.
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Question 691 Mark
The following numbers are obviously not perfect square. Give reason.
64000
Answer
The given number 64000 ends with 0, so it cannot be a perfect square due to odd number of zeroes.
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Question 701 Mark
The following numbers are obviously not perfect square. Give reason.
222222
Answer
The given number 222222 ends with 2, which is not of the end digit of 0, 1, 4, 5, 6 or 9, so it cannot be a perfect square.
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Question 711 Mark
The following numbers are obviously not perfect square. Give reason.
7928
Answer
The given number 7928 ends with 8, which is not of the end digit of 0, 1, 4, 5, 6 or 9, so it cannot be a perfect square.
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Question 721 Mark
The following numbers are obviously not perfect square. Give reason.
23453
Answer
The given number 23453 ends with 3, which is not of the end digit of $0,1,4,5,6$ or 9, so it cannot be a perfect square.
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Question 731 Mark
The following numbers are obviously not perfect square. Give reason.
1057
Answer
The given number 1057 ends with 7, which is not of the end digit of $0,1,4,5,6$ or 9 , so it cannot be a perfect square.
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Question 821 Mark
What will be the unit digit of the square of the following numbers?
272
Answer
Given number is 272.
unit digit of $272=2$
So, the square of unit digit $=2^2=4$
Hence, unit digit of the square of unit digit of the given number is 4.
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Question 831 Mark
What will be the unit digit of the square of the following numbers?
81
Answer
Given number is 81
unit digit of $81=1$
So, the square of unit digit $=1^2=1$
Hence, unit digit of the square of unit digit of the given number is 1.
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Question 851 Mark
How is the repeated subtraction method in dividing two numbers and finding square roots different?
Answer
Same number is subtracted each time in division, but in finding square root, successive odd numbers are subtracted.
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Question 861 Mark
Are all squares natural numbers? Explain.
Answer
Yes, all squares are natural numbers because
(i) A square number $\text{m}$ can be expressed as $\text{x}^2$.
(ii) A square number is a positive number value which is obtained by multiplying a number twice.
(iii) Examples of square numbers are $1,4,9,16,25$, $\ldots\ldots$ all of which are natural numbers.
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Question 871 Mark
Find the sum of first $\text{n}$ odd natural numbers.
Answer
The sum of first $\text{n}$ odd natural numbers is $\text{n}^2.$
$\begin{array}{l}\text {e.g.}\quad 1+3+5+7=16=4^2 \\\Rightarrow \quad 1+3+5=9=3^2 \\\Rightarrow \quad 1+3=4=2^2\end{array}$
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Question 881 Mark
Find the sum of first 4 odd natural numbers and write the number whose square it is.
Answer
Sum of first 4 odd natural numbers is, $1+3+5+7=16.$ Hence, 16 is a square of 4.
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Question 891 Mark
How many perfect squares lie between 1 and 50?
Answer
$4,9,16,25,36$ and $49$ are six perfect squares which lie between 1 and 50.
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