Square Root Of 1140 In Simplest Radical Form

Simplify the square root of 1140 to its lowest radical form.

ANSWER: 2√285

2√285 is in the lowest radical form.

Simplified Radical Form of √1140

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 √1140, we need to divide into factors.

√1140 = √2 x √2 x √3 x √5 x √19

Step 2: List Perfect Squares

1 is a perfect square and divides 1140
4 is a perfect square and divides 1140

Step 3: Divide To Perfect Square

Divide 1140 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 1140 in its simplest form: 2√285

How do you simplify √1140

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 1140. Divide 1140 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√285.

Simplified Decimal Form of √1140

The square root of 1140 is approximately 33.764 when expressed in decimal form and you can find additive inverse of a decimal number.

Calculation Table:

Square Root Answer Calculation
√17 Square root of 17 is the simplest radical form. √17
√93 Square root of 93 is the simplest radical form. √3 x √31
√64 8√1 √2 x √2 x √2 x √2 x √2 x √2
√291 Square root of 291 is the simplest radical form. √3 x √97
√303 Square root of 303 is the simplest radical form. √3 x √101
√129 Square root of 129 is the simplest radical form. √3 x √43
√9233 Square root of 9233 is the simplest radical form. √7 x √1319
√2198 Square root of 2198 is the simplest radical form. √2 x √7 x √157
√3673 Square root of 3673 is the simplest radical form. √3673

Convert any root forms to simplest radical form.

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