Square Root Of 7640 In Simplest Radical Form

Simplify the square root of 7640 to its lowest radical form.

ANSWER: 2√1910

2√1910 is in the lowest radical form.

Simplified Radical Form of √7640

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 √7640, we need to divide into factors.

√7640 = √2 x √2 x √2 x √5 x √191

Step 2: List Perfect Squares

1 is a perfect square and divides 7640
4 is a perfect square and divides 7640

Step 3: Divide To Perfect Square

Divide 7640 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 7640 in its simplest form: 2√1910

How do you simplify √7640

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 7640. Divide 7640 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√1910.

Simplified Decimal Form of √7640

The square root of 7640 is approximately 87.407 when expressed in decimal form.

Calculation Table:

Square Root Answer Calculation
√37 Square root of 37 is the simplest radical form. √37
√9 3√1 √3 x √3
√55 Square root of 55 is the simplest radical form. √5 x √11
√894 Square root of 894 is the simplest radical form. √2 x √3 x √149
√946 Square root of 946 is the simplest radical form. √2 x √11 x √43
√614 Square root of 614 is the simplest radical form. √2 x √307
√3803 Square root of 3803 is the simplest radical form. √3803
√5650 5√226 √2 x √5 x √5 x √113
√7649 Square root of 7649 is the simplest radical form. √7649

Convert any root forms to simplest radical form.

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