Question

The square root of 2025 is

Answer 1

Step-by-step explanation:

45×45=2025

so

45

mark as brilliant thanks for all question mark

Answer 2

$\bf \small \underline {\underline{Solution :-}}$

There are two ways to find the square root of 2025. Let's understand the two ways with their steps.

$\sf\underline{{✇ \: Prime \: factorisation \:- }{ \: }}$

The steps to find the square root by prime factorisation are :

• Write the number as a product of its prime factors.
• Make pairs of equal prime factors.
• Take obe factor from each pair and multiply them.

On prime factorisation,

∴ 2025 = 3 × 3 × 3 × 3 × 5 × 5

➯ (3 × 3) × (3 × 3) × (5 × 5)

∴ √2025 = 3 × 3 × 5 = 45

➻ Refer to the attachment as well.

Hence, the square root of 2025 is 45.

$\sf\underline{{✇ \: Alternative \: method \:- }{ \: }}$

You can also express the number as a product of powers of the prime factors. Taking half of each index of those powers and then finding the product of the factors will give the square root.

Alternative way -

2025 = 3⁴ × 5²

$∴ √2025 = {3}^{4 / 2} \times {5}^{2 / 2}$

➯ 3² × 5¹

➯ 9 × 5

➻ 45

∴ The square root of 2025 is 45.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬