Square Root Of 9 In Simplest Radical Form
Simplify the square root of 9 to its lowest radical form.ANSWER: 3√1
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
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 √9, we need to divide into factors.
√9 = √3 x √3Step 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 and you can find additive inverse of a decimal number.
Calculation Table:
Square Root | Answer | Calculation |
---|---|---|
√88 | 2√22 | √2 x √2 x √2 x √11 |
√17 | Square root of 17 is the simplest radical form. | √17 |
√14 | Square root of 14 is the simplest radical form. | √2 x √7 |
√306 | 3√34 | √2 x √3 x √3 x √17 |
√628 | 2√157 | √2 x √2 x √157 |
√575 | 5√23 | √5 x √5 x √23 |
√3899 | Square root of 3899 is the simplest radical form. | √7 x √557 |
√8180 | 2√2045 | √2 x √2 x √5 x √409 |
√9533 | Square root of 9533 is the simplest radical form. | √9533 |