Question

How do you find the square root of \[15\]?

Answer 1

Hint: For finding the square root of a given number, firstly we will simplify the expression of the square root of given number involving finding factors. This means we are trying to find the two whole numbers that when we multiplied we get the number .Then continue factoring until you have all prime numbers. To simplify a number underneath the square root symbol, it is very useful to keep factoring the factors unit. The only factors using exponents. Then move bases outside of the square root if possible, the rule for moving bass outside of the symbol is to divide the exponent power \[2\].

Complete step-by-step answer:
 Step1: We find the square root of \[15\]. Square root of \[15\] can be written as \[\sqrt {15} \] .Firstly we find the number , when it multiplied we get \[15\], \[3\] and \[5\] is two number, it multiplied we get \[15\]
So, we can write \[\sqrt {15} = \sqrt {3 \times 5} \].
Step2: Further find the prime number (factors) because it is very useful to keep factoring the factors until the only factors that are left are prime numbers.
So, \[30\] but here \[3\]has no factor as well as \[5\] has no factor so we can write as its \[15 = {\text{ }}3 \times 5\]
Step3: Then the repeated factors can be rewritten the more efficiently by using exponents but we don’t have repeated factors of \[3\] and \[5\].
Therefore \[\sqrt {15} = \sqrt {3 \times 5} \]
Step4: Further we can give the underneath root symbol, the each of the factors(number)
Therefore \[\sqrt {3 \times 5} = \sqrt 3 \times \sqrt 5 \]
We know that the \[\sqrt 3 \] is approximately \[1.73\]and \[\sqrt 5 \] is approximately \[2.24\].
Therefore we can write as \[\sqrt {3 \times 5} = \sqrt 3 \times \sqrt 5 \]\[ = 1.73 \times 2.24 = 3.8752\]
Hence \[\sqrt {15} = 3.8752\]
So, square root of \[15\] is \[3.8752\].

Note: Square root is the inverse option of squaring the positive square root of a number is denoted by the symbol \[\sqrt {} \] .Example \[\sqrt 9 = 3\] .To find the square root of a decimal number we put bars on the integral part of the number in usual manner.