Square Root Of 692 In Simplest Radical Form

Simplify the square root of 692 to its lowest radical form.

ANSWER: 2√173

2√173 is in the lowest radical form.

Simplified Radical Form of √692

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 √692, we need to divide into factors.

√692 = √2 x √2 x √173

Step 2: List Perfect Squares

1 is a perfect square and divides 692
4 is a perfect square and divides 692

Step 3: Divide To Perfect Square

Divide 692 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 692 in its simplest form: 2√173

How do you simplify √692

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 692. Divide 692 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√173.

Simplified Decimal Form of √692

The square root of 692 is approximately 26.306 when expressed in decimal form.

Calculation Table:

Square Root Answer Calculation
√75 5√3 √3 x √5 x √5
√34 Square root of 34 is the simplest radical form. √2 x √17
√23 Square root of 23 is the simplest radical form. √23
√802 Square root of 802 is the simplest radical form. √2 x √401
√854 Square root of 854 is the simplest radical form. √2 x √7 x √61
√964 2√241 √2 x √2 x √241
√6878 Square root of 6878 is the simplest radical form. √2 x √19 x √181
√1483 Square root of 1483 is the simplest radical form. √1483
√1195 Square root of 1195 is the simplest radical form. √5 x √239

Convert any root forms to simplest radical form.

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