Square Root Of 632 In Simplest Radical Form

Simplify the square root of 632 to its lowest radical form.

ANSWER: 2√158

2√158 is in the lowest radical form.

Simplified Radical Form of √632

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 √632, we need to divide into factors.

√632 = √2 x √2 x √2 x √79

Step 2: List Perfect Squares

1 is a perfect square and divides 632
4 is a perfect square and divides 632

Step 3: Divide To Perfect Square

Divide 632 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 632 in its simplest form: 2√158

How do you simplify √632

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 632. Divide 632 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√158.

Simplified Decimal Form of √632

The square root of 632 is approximately 25.14 when expressed in decimal form and you can find additive inverse of a decimal number.

Calculation Table:

Square Root Answer Calculation
√40 2√10 √2 x √2 x √2 x √5
√31 Square root of 31 is the simplest radical form. √31
√53 Square root of 53 is the simplest radical form. √53
√498 Square root of 498 is the simplest radical form. √2 x √3 x √83
√784 28√1 √2 x √2 x √2 x √2 x √7 x √7
√146 Square root of 146 is the simplest radical form. √2 x √73
√7305 Square root of 7305 is the simplest radical form. √3 x √5 x √487
√2090 Square root of 2090 is the simplest radical form. √2 x √5 x √11 x √19
√8614 Square root of 8614 is the simplest radical form. √2 x √59 x √73

Convert any root forms to simplest radical form.

About - Privacy - Contact - Disclaimer

Copyright 2024 - © Simplest Radical Form