Square Root Of 8 In Simplest Radical Form

Simplify the square root of 8 to its lowest radical form.

ANSWER: 2√2

2√2 is in the lowest radical form.

Simplified Radical Form of √8

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 √8, we need to divide into factors.

√8 = √2 x √2 x √2

Step 2: List Perfect Squares

1 is a perfect square and divides 8
4 is a perfect square and divides 8

Step 3: Divide To Perfect Square

Divide 8 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 8 in its simplest form: 2√2

How do you simplify √8

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 8. Divide 8 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√2.

Simplified Decimal Form of √8

The square root of 8 is approximately 2.828 when expressed in decimal form.

Calculation Table:

Square Root Answer Calculation
√62 Square root of 62 is the simplest radical form. √2 x √31
√75 5√3 √3 x √5 x √5
√39 Square root of 39 is the simplest radical form. √3 x √13
√836 2√209 √2 x √2 x √11 x √19
√352 4√22 √2 x √2 x √2 x √2 x √2 x √11
√453 Square root of 453 is the simplest radical form. √3 x √151
√2228 2√557 √2 x √2 x √557
√4422 Square root of 4422 is the simplest radical form. √2 x √3 x √11 x √67
√1599 Square root of 1599 is the simplest radical form. √3 x √13 x √41

Convert any root forms to simplest radical form.

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