Square Root Of 916 In Simplest Radical Form

Simplify the square root of 916 to its lowest radical form.

ANSWER: 2√229

2√229 is in the lowest radical form.

Simplified Radical Form of √916

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 √916, we need to divide into factors.

√916 = √2 x √2 x √229

Step 2: List Perfect Squares

1 is a perfect square and divides 916
4 is a perfect square and divides 916

Step 3: Divide To Perfect Square

Divide 916 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 916 in its simplest form: 2√229

How do you simplify √916

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 916. Divide 916 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√229.

Simplified Decimal Form of √916

The square root of 916 is approximately 30.265 when expressed in decimal form.

Calculation Table:

Square Root Answer Calculation
√29 Square root of 29 is the simplest radical form. √29
√69 Square root of 69 is the simplest radical form. √3 x √23
√53 Square root of 53 is the simplest radical form. √53
√725 5√29 √5 x √5 x √29
√783 3√87 √3 x √3 x √3 x √29
√465 Square root of 465 is the simplest radical form. √3 x √5 x √31
√5233 Square root of 5233 is the simplest radical form. √5233
√1655 Square root of 1655 is the simplest radical form. √5 x √331
√9376 4√586 √2 x √2 x √2 x √2 x √2 x √293

Convert any root forms to simplest radical form.

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