Square Root Of 7508 In Simplest Radical Form

Simplify the square root of 7508 to its lowest radical form.

ANSWER: 2√1877

2√1877 is in the lowest radical form.

Simplified Radical Form of √7508

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


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 √7508, we need to divide into factors.

√7508 = √2 x √2 x √1877

Step 2: List Perfect Squares

1 is a perfect square and divides 7508
4 is a perfect square and divides 7508

Step 3: Divide To Perfect Square

Divide 7508 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 7508 in its simplest form: 2√1877

How do you simplify √7508

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 7508. Divide 7508 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 2√1877.

Simplified Decimal Form of √7508

The square root of 7508 is approximately 86.649 when expressed in decimal form.

Calculation Table:

Square Root Answer Calculation
√21 Square root of 21 is the simplest radical form. √3 x √7
√77 Square root of 77 is the simplest radical form. √7 x √11
√6 Square root of 6 is the simplest radical form. √2 x √3
√144 12√1 √2 x √2 x √2 x √2 x √3 x √3
√823 Square root of 823 is the simplest radical form. √823
√196 14√1 √2 x √2 x √7 x √7
√8052 2√2013 √2 x √2 x √3 x √11 x √61
√3465 3√385 √3 x √3 x √5 x √7 x √11
√8427 53√3 √3 x √53 x √53

Convert any root forms to simplest radical form.

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