Square Root Of 9 In Simplest Radical Form

Simplify the square root of 9 to its lowest radical form.


3√1 is in the lowest radical form.

Simplified Radical Form of √9

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


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 √9, we need to divide into factors.

√9 = √3 x √3

Step 2: List Perfect Squares

1 is a perfect square and divides 9
9 is a perfect square and divides 9

Step 3: Divide To Perfect Square

Divide 9 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 9 in its simplest form: 3√1

How do you simplify √9

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 9. Divide 9 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 3√1.

Simplified Decimal Form of √9

The square root of 9 is approximately 3 when expressed in decimal form.

Calculation Table:

Square Root Answer Calculation
√47 Square root of 47 is the simplest radical form. √47
√54 3√6 √2 x √3 x √3 x √3
√20 2√5 √2 x √2 x √5
√638 Square root of 638 is the simplest radical form. √2 x √11 x √29
√377 Square root of 377 is the simplest radical form. √13 x √29
√578 17√2 √2 x √17 x √17
√9676 2√2419 √2 x √2 x √41 x √59
√4220 2√1055 √2 x √2 x √5 x √211
√1329 Square root of 1329 is the simplest radical form. √3 x √443

Convert any root forms to simplest radical form.

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