Square Root Of 9724 In Simplest Radical Form

Simplify the square root of 9724 to its lowest radical form.

ANSWER: 2√2431

2√2431 is in the lowest radical form.

Simplified Radical Form of √9724

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 √9724, we need to divide into factors.

√9724 = √2 x √2 x √11 x √13 x √17

Step 2: List Perfect Squares

1 is a perfect square and divides 9724
4 is a perfect square and divides 9724

Step 3: Divide To Perfect Square

Divide 9724 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 9724 in its simplest form: 2√2431

How do you simplify √9724

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 9724. Divide 9724 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√2431.

Simplified Decimal Form of √9724

The square root of 9724 is approximately 98.61 when expressed in decimal form.

Calculation Table:

Square Root Answer Calculation
√13 Square root of 13 is the simplest radical form. √13
√28 2√7 √2 x √2 x √7
√5 Square root of 5 is the simplest radical form. √5
√971 Square root of 971 is the simplest radical form. √971
√310 Square root of 310 is the simplest radical form. √2 x √5 x √31
√867 17√3 √3 x √17 x √17
√1887 Square root of 1887 is the simplest radical form. √3 x √17 x √37
√7204 2√1801 √2 x √2 x √1801
√9121 Square root of 9121 is the simplest radical form. √7 x √1303

Convert any root forms to simplest radical form.

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