Square Root Of 6597 In Simplest Radical Form

Simplify the square root of 6597 to its lowest radical form.

ANSWER: 3√733

3√733 is in the lowest radical form.

Simplified Radical Form of √6597

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 √6597, we need to divide into factors.

√6597 = √3 x √3 x √733

Step 2: List Perfect Squares

1 is a perfect square and divides 6597
9 is a perfect square and divides 6597

Step 3: Divide To Perfect Square

Divide 6597 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 6597 in its simplest form: 3√733

How do you simplify √6597

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 6597. Divide 6597 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√733.

Simplified Decimal Form of √6597

The square root of 6597 is approximately 81.222 when expressed in decimal form.

Calculation Table:

Square Root Answer Calculation
√75 5√3 √3 x √5 x √5
√37 Square root of 37 is the simplest radical form. √37
√52 2√13 √2 x √2 x √13
√349 Square root of 349 is the simplest radical form. √349
√838 Square root of 838 is the simplest radical form. √2 x √419
√926 Square root of 926 is the simplest radical form. √2 x √463
√6615 21√15 √3 x √3 x √3 x √5 x √7 x √7
√3149 Square root of 3149 is the simplest radical form. √47 x √67
√7771 Square root of 7771 is the simplest radical form. √19 x √409

Convert any root forms to simplest radical form.

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