Square Root Of 343000 In Simplest Radical Form
Simplify the square root of 343000 to its lowest radical form.ANSWER: 70√70
70√70 is in the lowest radical form.
Simplified Radical Form of √343000
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 √343000, we need to divide into factors.
√343000 = √2 x √2 x √2 x √5 x √5 x √5 x √7 x √7 x √7Step 2: List Perfect Squares
1 is a perfect square and divides 343000
4 is a perfect square and divides 343000
25 is a perfect square and divides 343000
49 is a perfect square and divides 343000
100 is a perfect square and divides 343000
196 is a perfect square and divides 343000
1225 is a perfect square and divides 343000
4900 is a perfect square and divides 343000
Step 3: Divide To Perfect Square
Divide 343000 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 343000 in its simplest form: 70√70
How do you simplify √343000
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 343000. Divide 343000 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 70√70.
Simplified Decimal Form of √343000
The square root of 343000 is approximately 585.662 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √10 | Square root of 10 is the simplest radical form. | √2 x √5 |
| √26 | Square root of 26 is the simplest radical form. | √2 x √13 |
| √57 | Square root of 57 is the simplest radical form. | √3 x √19 |
| √338 | 13√2 | √2 x √13 x √13 |
| √474 | Square root of 474 is the simplest radical form. | √2 x √3 x √79 |
| √611 | Square root of 611 is the simplest radical form. | √13 x √47 |
| √5450 | 5√218 | √2 x √5 x √5 x √109 |
| √4162 | Square root of 4162 is the simplest radical form. | √2 x √2081 |
| √1578 | Square root of 1578 is the simplest radical form. | √2 x √3 x √263 |