Square Root Of 71639296 In Simplest Radical Form
Simplify the square root of 71639296 to its lowest radical form.ANSWER: 8464√1
8464√1 is in the lowest radical form.
Simplified Radical Form of √71639296
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 √71639296, we need to divide into factors.
√71639296 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √23 x √23 x √23 x √23Step 2: List Perfect Squares
1 is a perfect square and divides 71639296
4 is a perfect square and divides 71639296
16 is a perfect square and divides 71639296
64 is a perfect square and divides 71639296
256 is a perfect square and divides 71639296
529 is a perfect square and divides 71639296
2116 is a perfect square and divides 71639296
8464 is a perfect square and divides 71639296
33856 is a perfect square and divides 71639296
135424 is a perfect square and divides 71639296
279841 is a perfect square and divides 71639296
1119364 is a perfect square and divides 71639296
4477456 is a perfect square and divides 71639296
17909824 is a perfect square and divides 71639296
71639296 is a perfect square and divides 71639296
Step 3: Divide To Perfect Square
Divide 71639296 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 71639296 in its simplest form: 8464√1
How do you simplify √71639296
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 71639296. Divide 71639296 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 8464√1.
Simplified Decimal Form of √71639296
The square root of 71639296 is approximately 8464 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √97 | Square root of 97 is the simplest radical form. | √97 |
| √74 | Square root of 74 is the simplest radical form. | √2 x √37 |
| √22 | Square root of 22 is the simplest radical form. | √2 x √11 |
| √399 | Square root of 399 is the simplest radical form. | √3 x √7 x √19 |
| √795 | Square root of 795 is the simplest radical form. | √3 x √5 x √53 |
| √654 | Square root of 654 is the simplest radical form. | √2 x √3 x √109 |
| √4288 | 8√67 | √2 x √2 x √2 x √2 x √2 x √2 x √67 |
| √3721 | 61√1 | √61 x √61 |
| √9538 | Square root of 9538 is the simplest radical form. | √2 x √19 x √251 |