Square Root Of 328509 In Simplest Radical Form

Simplify the square root of 328509 to its lowest radical form.

ANSWER: 69√69

69√69 is in the lowest radical form.

Simplified Radical Form of √328509

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 √328509, we need to divide into factors.

√328509 = √3 x √3 x √3 x √23 x √23 x √23

Step 2: List Perfect Squares

1 is a perfect square and divides 328509
9 is a perfect square and divides 328509
529 is a perfect square and divides 328509
4761 is a perfect square and divides 328509

Step 3: Divide To Perfect Square

Divide 328509 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 328509 in its simplest form: 69√69

How do you simplify √328509

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 328509. Divide 328509 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 69√69.

Simplified Decimal Form of √328509

The square root of 328509 is approximately 573.157 when expressed in decimal form.

Calculation Table:

Square Root Answer Calculation
√46 Square root of 46 is the simplest radical form. √2 x √23
√42 Square root of 42 is the simplest radical form. √2 x √3 x √7
√7 Square root of 7 is the simplest radical form. √7
√934 Square root of 934 is the simplest radical form. √2 x √467
√480 4√30 √2 x √2 x √2 x √2 x √2 x √3 x √5
√135 3√15 √3 x √3 x √3 x √5
√7086 Square root of 7086 is the simplest radical form. √2 x √3 x √1181
√6724 82√1 √2 x √2 x √41 x √41
√7077 Square root of 7077 is the simplest radical form. √3 x √7 x √337

Convert any root forms to simplest radical form.

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