Square Root Of 1152 In Simplest Radical Form
Simplify the square root of 1152 to its lowest radical form.ANSWER: 24√2
24√2 is in the lowest radical form.
Simplified Radical Form of √1152
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 √1152, we need to divide into factors.
√1152 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √3 x √3Step 2: List Perfect Squares
1 is a perfect square and divides 1152
4 is a perfect square and divides 1152
9 is a perfect square and divides 1152
16 is a perfect square and divides 1152
36 is a perfect square and divides 1152
64 is a perfect square and divides 1152
144 is a perfect square and divides 1152
576 is a perfect square and divides 1152
Step 3: Divide To Perfect Square
Divide 1152 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 1152 in its simplest form: 24√2
How do you simplify √1152
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 1152. Divide 1152 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√2.
Simplified Decimal Form of √1152
The square root of 1152 is approximately 33.941 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √72 | 6√2 | √2 x √2 x √2 x √3 x √3 |
| √90 | 3√10 | √2 x √3 x √3 x √5 |
| √88 | 2√22 | √2 x √2 x √2 x √11 |
| √575 | 5√23 | √5 x √5 x √23 |
| √895 | Square root of 895 is the simplest radical form. | √5 x √179 |
| √843 | Square root of 843 is the simplest radical form. | √3 x √281 |
| √9784 | 2√2446 | √2 x √2 x √2 x √1223 |
| √4036 | 2√1009 | √2 x √2 x √1009 |
| √7945 | Square root of 7945 is the simplest radical form. | √5 x √7 x √227 |