Square Root Of 8 In Simplest Radical Form
Simplify the square root of 8 to its lowest radical form.ANSWER: 2√2
2√2 is in the lowest radical form.
Simplified Radical Form of √8
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 √8, we need to divide into factors.
√8 = √2 x √2 x √2Step 2: List Perfect Squares
1 is a perfect square and divides 8
4 is a perfect square and divides 8
Step 3: Divide To Perfect Square
Divide 8 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 8 in its simplest form: 2√2
How do you simplify √8
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 8. Divide 8 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 2√2.
Simplified Decimal Form of √8
The square root of 8 is approximately 2.828 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
Square Root | Answer | Calculation |
---|---|---|
√80 | 4√5 | √2 x √2 x √2 x √2 x √5 |
√90 | 3√10 | √2 x √3 x √3 x √5 |
√68 | 2√17 | √2 x √2 x √17 |
√783 | 3√87 | √3 x √3 x √3 x √29 |
√839 | Square root of 839 is the simplest radical form. | √839 |
√727 | Square root of 727 is the simplest radical form. | √727 |
√1106 | Square root of 1106 is the simplest radical form. | √2 x √7 x √79 |
√8519 | Square root of 8519 is the simplest radical form. | √7 x √1217 |
√6995 | Square root of 6995 is the simplest radical form. | √5 x √1399 |