Square Root Of 9312 In Simplest Radical Form

Simplify the square root of 9312 to its lowest radical form.

ANSWER: 4√582

4√582 is in the lowest radical form.

Simplified Radical Form of √9312

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 √9312, we need to divide into factors.

√9312 = √2 x √2 x √2 x √2 x √2 x √3 x √97

Step 2: List Perfect Squares

1 is a perfect square and divides 9312
4 is a perfect square and divides 9312
16 is a perfect square and divides 9312

Step 3: Divide To Perfect Square

Divide 9312 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 9312 in its simplest form: 4√582

How do you simplify √9312

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 9312. Divide 9312 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 4√582.

Simplified Decimal Form of √9312

The square root of 9312 is approximately 96.499 when expressed in decimal form.

Calculation Table:

Square Root Answer Calculation
√98 7√2 √2 x √7 x √7
√89 Square root of 89 is the simplest radical form. √89
√78 Square root of 78 is the simplest radical form. √2 x √3 x √13
√193 Square root of 193 is the simplest radical form. √193
√946 Square root of 946 is the simplest radical form. √2 x √11 x √43
√919 Square root of 919 is the simplest radical form. √919
√8389 Square root of 8389 is the simplest radical form. √8389
√8671 Square root of 8671 is the simplest radical form. √13 x √23 x √29
√7145 Square root of 7145 is the simplest radical form. √5 x √1429

Convert any root forms to simplest radical form.

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