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 |
---|---|---|
√37 | Square root of 37 is the simplest radical form. | √37 |
√39 | Square root of 39 is the simplest radical form. | √3 x √13 |
√79 | Square root of 79 is the simplest radical form. | √79 |
√283 | Square root of 283 is the simplest radical form. | √283 |
√957 | Square root of 957 is the simplest radical form. | √3 x √11 x √29 |
√278 | Square root of 278 is the simplest radical form. | √2 x √139 |
√8108 | 2√2027 | √2 x √2 x √2027 |
√6037 | Square root of 6037 is the simplest radical form. | √6037 |
√1704 | 2√426 | √2 x √2 x √2 x √3 x √71 |