Square Root Of 6705 In Simplest Radical Form

Simplify the square root of 6705 to its lowest radical form.

ANSWER: 3√745

3√745 is in the lowest radical form.

Simplified Radical Form of √6705

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 √6705, we need to divide into factors.

√6705 = √3 x √3 x √5 x √149

Step 2: List Perfect Squares

1 is a perfect square and divides 6705
9 is a perfect square and divides 6705

Step 3: Divide To Perfect Square

Divide 6705 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 6705 in its simplest form: 3√745

How do you simplify √6705

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 6705. Divide 6705 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√745.

Simplified Decimal Form of √6705

The square root of 6705 is approximately 81.884 when expressed in decimal form and you can find additive inverse of a decimal number.

Calculation Table:

Square Root Answer Calculation
√93 Square root of 93 is the simplest radical form. √3 x √31
√34 Square root of 34 is the simplest radical form. √2 x √17
√58 Square root of 58 is the simplest radical form. √2 x √29
√539 7√11 √7 x √7 x √11
√694 Square root of 694 is the simplest radical form. √2 x √347
√969 Square root of 969 is the simplest radical form. √3 x √17 x √19
√7746 Square root of 7746 is the simplest radical form. √2 x √3 x √1291
√2916 54√1 √2 x √2 x √3 x √3 x √3 x √3 x √3 x √3
√8871 Square root of 8871 is the simplest radical form. √3 x √2957

Convert any root forms to simplest radical form.

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