Question

If \[\sqrt{2}=1.414\], then the value of \[\sqrt{8}\] is?

Answer 1

Hint: In this problem, we have to find the value of \[\sqrt{8}\] if \[\sqrt{2}=1.414\]. We can first simplify the term \[\sqrt{8}\]. We can first write the term \[\sqrt{8}\] as \[\sqrt{2\times 2\times 2}\] . We can then use the formula \[\sqrt{a\times a\times a}=\sqrt{a}\times \sqrt{a}\times \sqrt{a}\] and separate the terms, we can then substitute the given value and simplify them, we can multiply the terms step by step to find the total value of the given square root term to get the value of the given term \[\sqrt{8}\].

Complete step by step answer:
Here we have to find the value of \[\sqrt{8}\] if \[\sqrt{2}=1.414\].
We can now write the term \[\sqrt{8}\] as,
\[\Rightarrow \sqrt{8}=\sqrt{2\times 2\times 2}\]
We can now separate the terms inside the square root with the terms with individual square root using the formula \[\sqrt{a\times a\times a}=\sqrt{a}\times \sqrt{a}\times \sqrt{a}\], we get
\[\Rightarrow \sqrt{2\times 2\times 2}=\sqrt{2}\times \sqrt{2}\times \sqrt{2}\]
We know that we are given the value of square root of 2, we can now substitute it in the above step, we get
\[\Rightarrow \sqrt{2}\times \sqrt{2}\times \sqrt{2}=1.414\times 1.414\times 1.414\]
We can now multiply the terms in the above step, we get
\[\Rightarrow 2\times 1.414\]
We can further simplify by multiplying the above terms, we get
\[\Rightarrow \sqrt{8}=2.828\]
Therefore, the value of \[\sqrt{8}\] if \[\sqrt{2}=1.414\] is 2.828.

Note: We should always remember that the formula to separate the whole square root into its equivalent individual square roots is \[\sqrt{a\times a\times a}=\sqrt{a}\times \sqrt{a}\times \sqrt{a}\]. We can then substitute the value of the individual square root and multiply the terms to get the required value. We can multiply the terms step by step to find the total value of the given square root term.