Square Root Of 2996 In Simplest Radical Form

Simplify the square root of 2996 to its lowest radical form.

ANSWER: 2√749

2√749 is in the lowest radical form.

Simplified Radical Form of √2996

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 √2996, we need to divide into factors.

√2996 = √2 x √2 x √7 x √107

Step 2: List Perfect Squares

1 is a perfect square and divides 2996
4 is a perfect square and divides 2996

Step 3: Divide To Perfect Square

Divide 2996 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 2996 in its simplest form: 2√749

How do you simplify √2996

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 2996. Divide 2996 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√749.

Simplified Decimal Form of √2996

The square root of 2996 is approximately 54.736 when expressed in decimal form.

Calculation Table:

Square Root Answer Calculation
√10 Square root of 10 is the simplest radical form. √2 x √5
√39 Square root of 39 is the simplest radical form. √3 x √13
√53 Square root of 53 is the simplest radical form. √53
√293 Square root of 293 is the simplest radical form. √293
√648 18√2 √2 x √2 x √2 x √3 x √3 x √3 x √3
√518 Square root of 518 is the simplest radical form. √2 x √7 x √37
√8923 Square root of 8923 is the simplest radical form. √8923
√9827 Square root of 9827 is the simplest radical form. √31 x √317
√3762 3√418 √2 x √3 x √3 x √11 x √19

Convert any root forms to simplest radical form.

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