Square Root Of 8172 In Simplest Radical Form

Simplify the square root of 8172 to its lowest radical form.

ANSWER: 6√227

6√227 is in the lowest radical form.

Simplified Radical Form of √8172

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 √8172, we need to divide into factors.

√8172 = √2 x √2 x √3 x √3 x √227

Step 2: List Perfect Squares

1 is a perfect square and divides 8172
4 is a perfect square and divides 8172
9 is a perfect square and divides 8172
36 is a perfect square and divides 8172

Step 3: Divide To Perfect Square

Divide 8172 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 8172 in its simplest form: 6√227

How do you simplify √8172

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 8172. Divide 8172 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 6√227.

Simplified Decimal Form of √8172

The square root of 8172 is approximately 90.399 when expressed in decimal form.

Calculation Table:

Square Root Answer Calculation
√98 7√2 √2 x √7 x √7
√35 Square root of 35 is the simplest radical form. √5 x √7
√93 Square root of 93 is the simplest radical form. √3 x √31
√548 2√137 √2 x √2 x √137
√926 Square root of 926 is the simplest radical form. √2 x √463
√689 Square root of 689 is the simplest radical form. √13 x √53
√8815 Square root of 8815 is the simplest radical form. √5 x √41 x √43
√5333 Square root of 5333 is the simplest radical form. √5333
√5154 Square root of 5154 is the simplest radical form. √2 x √3 x √859

Convert any root forms to simplest radical form.

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