Square Root Of 812 In Simplest Radical Form

Simplify the square root of 812 to its lowest radical form.

ANSWER: 2√203

2√203 is in the lowest radical form.

Simplified Radical Form of √812

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 √812, we need to divide into factors.

√812 = √2 x √2 x √7 x √29

Step 2: List Perfect Squares

1 is a perfect square and divides 812
4 is a perfect square and divides 812

Step 3: Divide To Perfect Square

Divide 812 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 812 in its simplest form: 2√203

How do you simplify √812

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 812. Divide 812 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√203.

Simplified Decimal Form of √812

The square root of 812 is approximately 28.496 when expressed in decimal form.

Calculation Table:

Square Root Answer Calculation
√48 4√3 √2 x √2 x √2 x √2 x √3
√74 Square root of 74 is the simplest radical form. √2 x √37
√48 4√3 √2 x √2 x √2 x √2 x √3
√294 7√6 √2 x √3 x √7 x √7
√452 2√113 √2 x √2 x √113
√493 Square root of 493 is the simplest radical form. √17 x √29
√7059 Square root of 7059 is the simplest radical form. √3 x √13 x √181
√4205 29√5 √5 x √29 x √29
√3755 Square root of 3755 is the simplest radical form. √5 x √751

Convert any root forms to simplest radical form.

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