Square Root Of 512000 In Simplest Radical Form

Simplify the square root of 512000 to its lowest radical form.

ANSWER: 320√5

320√5 is in the lowest radical form.

Simplified Radical Form of √512000

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 √512000, we need to divide into factors.

√512000 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √5 x √5 x √5

Step 2: List Perfect Squares

1 is a perfect square and divides 512000
4 is a perfect square and divides 512000
16 is a perfect square and divides 512000
25 is a perfect square and divides 512000
64 is a perfect square and divides 512000
100 is a perfect square and divides 512000
256 is a perfect square and divides 512000
400 is a perfect square and divides 512000
1024 is a perfect square and divides 512000
1600 is a perfect square and divides 512000
4096 is a perfect square and divides 512000
6400 is a perfect square and divides 512000
25600 is a perfect square and divides 512000
102400 is a perfect square and divides 512000

Step 3: Divide To Perfect Square

Divide 512000 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 512000 in its simplest form: 320√5

How do you simplify √512000

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 512000. Divide 512000 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 320√5.

Simplified Decimal Form of √512000

The square root of 512000 is approximately 715.542 when expressed in decimal form and you can find additive inverse of a decimal number.

Calculation Table:

Square Root Answer Calculation
√53 Square root of 53 is the simplest radical form. √53
√98 7√2 √2 x √7 x √7
√80 4√5 √2 x √2 x √2 x √2 x √5
√590 Square root of 590 is the simplest radical form. √2 x √5 x √59
√349 Square root of 349 is the simplest radical form. √349
√149 Square root of 149 is the simplest radical form. √149
√1098 3√122 √2 x √3 x √3 x √61
√4226 Square root of 4226 is the simplest radical form. √2 x √2113
√8021 Square root of 8021 is the simplest radical form. √13 x √617

Convert any root forms to simplest radical form.

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