Square Root Of 31640625 In Simplest Radical Form

Simplify the square root of 31640625 to its lowest radical form.

ANSWER: 5625√1

5625√1 is in the lowest radical form.

Simplified Radical Form of √31640625

One of the main facts used to simplify square roots is that the square root of a product is equal to the product of square roots: √(x×y) = √x×√y

Explanation:

When we find square root of any number, we take one number from each pair of the same numbers from its prime factorization and we multiply them.

Step 1: List Factors

To simplify √31640625, we need to divide into factors.

√31640625 = √3 x √3 x √3 x √3 x √5 x √5 x √5 x √5 x √5 x √5 x √5 x √5

Step 2: List Perfect Squares

1 is a perfect square and divides 31640625
9 is a perfect square and divides 31640625
25 is a perfect square and divides 31640625
81 is a perfect square and divides 31640625
225 is a perfect square and divides 31640625
625 is a perfect square and divides 31640625
2025 is a perfect square and divides 31640625
5625 is a perfect square and divides 31640625
15625 is a perfect square and divides 31640625
50625 is a perfect square and divides 31640625
140625 is a perfect square and divides 31640625
390625 is a perfect square and divides 31640625
1265625 is a perfect square and divides 31640625
3515625 is a perfect square and divides 31640625
31640625 is a perfect square and divides 31640625

Step 3: Divide To Perfect Square

Divide 31640625 by the largest perfect square you found in the previous step:

Step 4: Calculate The Square Root

Calculate the square root of the largest perfect square:

Final Step :

Put Steps 3 and 4 together to get the square root of 31640625 in its simplest form: 5625√1

How do you simplify √31640625

The general approach is to first check if it is a perfect square. If so, you have the answer. If it is not a perfect square, see if any of its factors are perfect squares, or can be combined to make square numbers.

Find the lowest prime number that can divide 31640625. Divide 31640625 repeatedly using the long division method till you reach 1.

A pair of factor 'twins' under a square root sign (radical) form a single factor outside of it.

Factors that do not have a twin remain under the radical. Multiply them back together and leave them in there.

So, the answer is 5625√1.

Simplified Decimal Form of √31640625

The square root of 31640625 is approximately 5625 when expressed in decimal form and you can find additive inverse of a decimal number.

Calculation Table: