How to find the square root of 8?
Understand the Problem
The question is asking how to calculate the square root of 8. This involves finding a number that, when multiplied by itself, equals 8. The square root can be simplified by expressing it in terms of its prime factors or using a calculator.
Answer
$2\sqrt{2}$
Answer for screen readers
The square root of 8 is $2\sqrt{2}$.
Steps to Solve
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Identify the square root To find the square root of 8, we want to find a number $x$ such that $x^2 = 8$.
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Simplify the expression We can simplify $\sqrt{8}$ by expressing it in terms of its prime factors: $$ 8 = 4 \times 2 = 2^2 \times 2 $$
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Extract the square root Now we can take the square root of each part: $$ \sqrt{8} = \sqrt{2^2 \times 2} = \sqrt{2^2} \times \sqrt{2} = 2\sqrt{2} $$
The square root of 8 is $2\sqrt{2}$.
More Information
The square root of 8 can also be approximated as $2.8284$ if calculated using a calculator. It's useful to know both the exact form and the decimal approximation.
Tips
- Miscalculating the square root by not simplifying properly.
- Forgetting that the square root can be expressed in terms of factors. Ensure to break down numbers into their prime factors to simplify.
