Square Root Of 1728 In Simplest Radical Form

Simplify the square root of 1728 to its lowest radical form.

ANSWER: 24√3

24√3 is in the lowest radical form.

Simplified Radical Form of √1728

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 √1728, we need to divide into factors.

√1728 = √2 x √2 x √2 x √2 x √2 x √2 x √3 x √3 x √3

Step 2: List Perfect Squares

1 is a perfect square and divides 1728
4 is a perfect square and divides 1728
9 is a perfect square and divides 1728
16 is a perfect square and divides 1728
36 is a perfect square and divides 1728
64 is a perfect square and divides 1728
144 is a perfect square and divides 1728
576 is a perfect square and divides 1728

Step 3: Divide To Perfect Square

Divide 1728 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 1728 in its simplest form: 24√3

How do you simplify √1728

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 1728. Divide 1728 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 24√3.

Simplified Decimal Form of √1728

The square root of 1728 is approximately 41.569 when expressed in decimal form.

Calculation Table: