Given , what is the value of ? (i) 15625 + 126 (ii) (iii) 15625 + 253 (iv) 15625 + 251 (v)

Question

Homi · Accepted Answer

An algebraic identity helps us find the square of a number easily.

Step 1 — Express the number

We are given the value of $125^2$ . We need to find the value of $126^2$ . We can write $126$ as the sum of two numbers. Let us write $126$ as $\mathbf{125 + 1}$ .

Step 2 — Apply the identity

We will use a special rule called an algebraic identity. This rule helps us square a sum of two numbers. The identity is $(a+b)^2 = a^2 + 2ab + b^2$ . Here, we can think of $a$ as $\mathbf{125}$ . We can think of $b$ as $\mathbf{1}$ . Let us substitute these values into the identity.

$126^2 = (125 + 1)^2$

$= 125^2 + (2 \times 125 \times 1) + 1^2$

$= 15625 + 250 + 1$

$= 15625 + 251$

$\boxed{15876}$

We found that $126^2$ is $\mathbf{15625 + 251}$ . This matches option (iv).

Answer

(iv) $15625 + 251$

Question 3

Answer

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