Square Root Of 45212176 In Simplest Radical Form
Simplify the square root of 45212176 to its lowest radical form.ANSWER: 6724√1
6724√1 is in the lowest radical form.
Simplified Radical Form of √45212176
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 √45212176, we need to divide into factors.
√45212176 = √2 x √2 x √2 x √2 x √41 x √41 x √41 x √41Step 2: List Perfect Squares
1 is a perfect square and divides 45212176
4 is a perfect square and divides 45212176
16 is a perfect square and divides 45212176
1681 is a perfect square and divides 45212176
6724 is a perfect square and divides 45212176
26896 is a perfect square and divides 45212176
2825761 is a perfect square and divides 45212176
11303044 is a perfect square and divides 45212176
45212176 is a perfect square and divides 45212176
Step 3: Divide To Perfect Square
Divide 45212176 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 45212176 in its simplest form: 6724√1
How do you simplify √45212176
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 45212176. Divide 45212176 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 6724√1.
Simplified Decimal Form of √45212176
The square root of 45212176 is approximately 6724 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 |
| √50 | 5√2 | √2 x √5 x √5 |
| √38 | Square root of 38 is the simplest radical form. | √2 x √19 |
| √615 | Square root of 615 is the simplest radical form. | √3 x √5 x √41 |
| √130 | Square root of 130 is the simplest radical form. | √2 x √5 x √13 |
| √864 | 12√6 | √2 x √2 x √2 x √2 x √2 x √3 x √3 x √3 |
| √5435 | Square root of 5435 is the simplest radical form. | √5 x √1087 |
| √9091 | Square root of 9091 is the simplest radical form. | √9091 |
| √3578 | Square root of 3578 is the simplest radical form. | √2 x √1789 |