Square Root Of 7506 In Simplest Radical Form

Simplify the square root of 7506 to its lowest radical form.

ANSWER: 3√834

3√834 is in the lowest radical form.

Simplified Radical Form of √7506

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 √7506, we need to divide into factors.

√7506 = √2 x √3 x √3 x √3 x √139

Step 2: List Perfect Squares

1 is a perfect square and divides 7506
9 is a perfect square and divides 7506

Step 3: Divide To Perfect Square

Divide 7506 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 7506 in its simplest form: 3√834

How do you simplify √7506

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 7506. Divide 7506 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 3√834.

Simplified Decimal Form of √7506

The square root of 7506 is approximately 86.637 when expressed in decimal form.

Calculation Table:

Square Root Answer Calculation
√57 Square root of 57 is the simplest radical form. √3 x √19
√39 Square root of 39 is the simplest radical form. √3 x √13
√82 Square root of 82 is the simplest radical form. √2 x √41
√922 Square root of 922 is the simplest radical form. √2 x √461
√326 Square root of 326 is the simplest radical form. √2 x √163
√177 Square root of 177 is the simplest radical form. √3 x √59
√6646 Square root of 6646 is the simplest radical form. √2 x √3323
√2152 2√538 √2 x √2 x √2 x √269
√3831 Square root of 3831 is the simplest radical form. √3 x √1277

Convert any root forms to simplest radical form.

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