Square Root Of 71639296 In Simplest Radical Form

Simplify the square root of 71639296 to its lowest radical form.

ANSWER: 8464√1

8464√1 is in the lowest radical form.

Simplified Radical Form of √71639296

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 √71639296, we need to divide into factors.

√71639296 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √23 x √23 x √23 x √23

Step 2: List Perfect Squares

1 is a perfect square and divides 71639296
4 is a perfect square and divides 71639296
16 is a perfect square and divides 71639296
64 is a perfect square and divides 71639296
256 is a perfect square and divides 71639296
529 is a perfect square and divides 71639296
2116 is a perfect square and divides 71639296
8464 is a perfect square and divides 71639296
33856 is a perfect square and divides 71639296
135424 is a perfect square and divides 71639296
279841 is a perfect square and divides 71639296
1119364 is a perfect square and divides 71639296
4477456 is a perfect square and divides 71639296
17909824 is a perfect square and divides 71639296
71639296 is a perfect square and divides 71639296

Step 3: Divide To Perfect Square

Divide 71639296 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 71639296 in its simplest form: 8464√1

How do you simplify √71639296

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 71639296. Divide 71639296 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 8464√1.

Simplified Decimal Form of √71639296

The square root of 71639296 is approximately 8464 when expressed in decimal form and you can find additive inverse of a decimal number.

Calculation Table:

Square Root Answer Calculation
√81 9√1 √3 x √3 x √3 x √3
√49 7√1 √7 x √7
√30 Square root of 30 is the simplest radical form. √2 x √3 x √5
√973 Square root of 973 is the simplest radical form. √7 x √139
√279 3√31 √3 x √3 x √31
√143 Square root of 143 is the simplest radical form. √11 x √13
√2465 Square root of 2465 is the simplest radical form. √5 x √17 x √29
√2595 Square root of 2595 is the simplest radical form. √3 x √5 x √173
√1753 Square root of 1753 is the simplest radical form. √1753

Convert any root forms to simplest radical form.

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