Question

What is 15 divided by the square root of 2?

Answer 1

Hint: Well, the answer for the given question is simply divide the 15 by root 2, it gives 10.6. we have two methods to follow either by eliminating the radical denominator or by calculating the value of root 2, before following the second method we need to know about the concept of power and roots.

Complete step by step solution:
The power is defined as the ‘a’ be any number and ‘n’ is natural number, then the formula is
\[a^{n} =a \times a \times a \times ........\]
Here a is called as ‘base’ and ‘n’ is known as index or exponent, and $a^n$ is called as exponential expression and it can be read as ‘a to the power of n’.
Root: when a number is multiplied with itself, the answer obtained is called a square of that number. Hence, the number itself becomes the root of its own multiple(resultant).
We can find out the square root of 2 using prime factorization method & division method
Let us solve the square root of 2 by using division method
Step 1: Choosing a number by identifying at least two ideal roots.
Step 2: Dividing 2 with chosen square root.
Step 3: As a result, take the average of the division result and multiply it by two.
Step 4: Utilize the outcome and repeat steps two and three before you achieve a satisfactory result.
The value of $\sqrt{2} =1.41421\overline{56862745098039}$
Simply, we can take an approximate value of $\sqrt{2} =1.414$
From the given question, we need to do is divide the 15 by the square root of 2
\[\dfrac{15}{\sqrt{2} } \Rightarrow \dfrac{15}{1.414} \Rightarrow {\rm 10.60820367751061}\]
The required answer is ${\rm 10.6}$
In another method, we can solve the given problem by eliminating the radical denominator, which we can do by multiplying the numerator and denominator by $\sqrt{2} $..
\[\dfrac{15}{\sqrt{2} } \Rightarrow \dfrac{15}{\sqrt{2} } .\dfrac{\sqrt{2} }{\sqrt{2} } \]
\[\Rightarrow \dfrac{15\sqrt{2} }{2} \Rightarrow 7.5\sqrt{2} \]
\[7.5\sqrt{2} \approx 10.6\]
The required solution is 10.6

Note: while solving this kind of questions, the common mistakes every student can do rationalizing the denominator. Not understanding the concept is also a mistake.