Square Root Of 3564 In Simplest Radical Form

Simplify the square root of 3564 to its lowest radical form.

ANSWER: 18√11

18√11 is in the lowest radical form.

Simplified Radical Form of √3564

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 √3564, we need to divide into factors.

√3564 = √2 x √2 x √3 x √3 x √3 x √3 x √11

Step 2: List Perfect Squares

1 is a perfect square and divides 3564
4 is a perfect square and divides 3564
9 is a perfect square and divides 3564
36 is a perfect square and divides 3564
81 is a perfect square and divides 3564
324 is a perfect square and divides 3564

Step 3: Divide To Perfect Square

Divide 3564 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 3564 in its simplest form: 18√11

How do you simplify √3564

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 3564. Divide 3564 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 18√11.

Simplified Decimal Form of √3564

The square root of 3564 is approximately 59.699 when expressed in decimal form.

Calculation Table:

Square Root Answer Calculation
√4 2√1 √2 x √2
√76 2√19 √2 x √2 x √19
√63 3√7 √3 x √3 x √7
√227 Square root of 227 is the simplest radical form. √227
√550 5√22 √2 x √5 x √5 x √11
√779 Square root of 779 is the simplest radical form. √19 x √41
√6616 2√1654 √2 x √2 x √2 x √827
√4259 Square root of 4259 is the simplest radical form. √4259
√1270 Square root of 1270 is the simplest radical form. √2 x √5 x √127

Convert any root forms to simplest radical form.

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