Evaluate 105 106 without multiplying directly. - Vidyadip

Question

Evaluate $105 \times 106$ without multiplying directly.

✓

Answer

Firstly, write $105$ as $100 + 5$ and $106$ as $100 + 6.$
$\therefore 105 \times 106 = (100 + 5) \times (100 + 6)$
$= (100)^2 + (5 + 6)100 + (5 \times 6)$
$[\because (x + a)(x + b) = x^2 + (a + b)x + ab]$
$= 10000+ 11\times100 + 30$
$= 10000 + 1100 + 30 = 11130$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Polynomials→Polynomials — all question types→MATHS STD 9 question papers→Rajasthan Board STD 9 question papers→Rajasthan Board question paper generator→

Similar questions

Find the following products: $(1 - x)(1 + x + x^2)$

Simplify the following expression : $(5+\sqrt{7})(5-\sqrt{7})$

Find four rational numbers lying between $\frac{3}{7}$ and $\frac{5}{7}.$

Factorise:$x^2 - x - 156$

Rationalise the denominator of the following:
$\frac{1+\sqrt{2}}{2-\sqrt{2}}$

The numbers of children in 10 families of a locality are 2, 4, 3, 4, 2, 3, 5, 1, 1, 5. Find the number of children per family.

Identify the following as rational or irrational numbers. Give the decimal representation of rational numbers:
$\sqrt{\Big(\frac{9}{27}\Big)}$

Simplify:$\Big(16^{-\frac{1}{5}}\Big)^{\frac{5}{2}}$

In the following equations, find which variables $x, y$ and $z$ etc. represent rational or irrational numbers:
$x^2 = 5$

Check the following are the solution of the equation 5x - 4y = 20.
(4, 0)