Square Root Of 64000 In Simplest Radical Form
Simplify the square root of 64000 to its lowest radical form.ANSWER: 80√10
80√10 is in the lowest radical form.
Simplified Radical Form of √64000
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 √64000, we need to divide into factors.
√64000 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √5 x √5 x √5Step 2: List Perfect Squares
1 is a perfect square and divides 64000
4 is a perfect square and divides 64000
16 is a perfect square and divides 64000
25 is a perfect square and divides 64000
64 is a perfect square and divides 64000
100 is a perfect square and divides 64000
256 is a perfect square and divides 64000
400 is a perfect square and divides 64000
1600 is a perfect square and divides 64000
6400 is a perfect square and divides 64000
Step 3: Divide To Perfect Square
Divide 64000 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 64000 in its simplest form: 80√10
How do you simplify √64000
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 64000. Divide 64000 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 80√10.
Simplified Decimal Form of √64000
The square root of 64000 is approximately 252.982 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √41 | Square root of 41 is the simplest radical form. | √41 |
| √91 | Square root of 91 is the simplest radical form. | √7 x √13 |
| √88 | 2√22 | √2 x √2 x √2 x √11 |
| √745 | Square root of 745 is the simplest radical form. | √5 x √149 |
| √324 | 18√1 | √2 x √2 x √3 x √3 x √3 x √3 |
| √398 | Square root of 398 is the simplest radical form. | √2 x √199 |
| √4940 | 2√1235 | √2 x √2 x √5 x √13 x √19 |
| √2635 | Square root of 2635 is the simplest radical form. | √5 x √17 x √31 |
| √1187 | Square root of 1187 is the simplest radical form. | √1187 |