Square Root Of 6889 In Simplest Radical Form

Simplify the square root of 6889 to its lowest radical form.

ANSWER: 83√1

83√1 is in the lowest radical form.

Simplified Radical Form of √6889

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 √6889, we need to divide into factors.

√6889 = √83 x √83

Step 2: List Perfect Squares

1 is a perfect square and divides 6889
6889 is a perfect square and divides 6889

Step 3: Divide To Perfect Square

Divide 6889 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 6889 in its simplest form: 83√1

How do you simplify √6889

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 6889. Divide 6889 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 83√1.

Simplified Decimal Form of √6889

The square root of 6889 is approximately 83 when expressed in decimal form.

Calculation Table:

Square Root Answer Calculation
√24 2√6 √2 x √2 x √2 x √3
√72 6√2 √2 x √2 x √2 x √3 x √3
√66 Square root of 66 is the simplest radical form. √2 x √3 x √11
√226 Square root of 226 is the simplest radical form. √2 x √113
√697 Square root of 697 is the simplest radical form. √17 x √41
√613 Square root of 613 is the simplest radical form. √613
√8794 Square root of 8794 is the simplest radical form. √2 x √4397
√7610 Square root of 7610 is the simplest radical form. √2 x √5 x √761
√4331 Square root of 4331 is the simplest radical form. √61 x √71

Convert any root forms to simplest radical form.

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