Square Root Of 7925 In Simplest Radical Form

Simplify the square root of 7925 to its lowest radical form.

ANSWER: 5√317

5√317 is in the lowest radical form.

Simplified Radical Form of √7925

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 √7925, we need to divide into factors.

√7925 = √5 x √5 x √317

Step 2: List Perfect Squares

1 is a perfect square and divides 7925
25 is a perfect square and divides 7925

Step 3: Divide To Perfect Square

Divide 7925 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 7925 in its simplest form: 5√317

How do you simplify √7925

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 7925. Divide 7925 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 5√317.

Simplified Decimal Form of √7925

The square root of 7925 is approximately 89.022 when expressed in decimal form and you can find additive inverse of a decimal number.

Calculation Table:

Square Root Answer Calculation
√99 3√11 √3 x √3 x √11
√29 Square root of 29 is the simplest radical form. √29
√26 Square root of 26 is the simplest radical form. √2 x √13
√283 Square root of 283 is the simplest radical form. √283
√879 Square root of 879 is the simplest radical form. √3 x √293
√959 Square root of 959 is the simplest radical form. √7 x √137
√6757 Square root of 6757 is the simplest radical form. √29 x √233
√4034 Square root of 4034 is the simplest radical form. √2 x √2017
√8369 Square root of 8369 is the simplest radical form. √8369

Convert any root forms to simplest radical form.

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