Question

How do you simplify (Square root of 75) + (Square root of 48) ?

Answer 1

Hint: According to the question, we need to first simplify the square roots. To simplify the square roots, we need to apply the prime factorization method for both the square roots. After the numbers are simplified, we can add them together, and get the answer.

Complete step by step answer:
The given expression is: (Square root of 75) + (Square root of 48)
We can also write it as: \[\sqrt {75} + \sqrt {48} \]
To solve this, we just have to calculate the square roots of the two and add them up. To find the square root of 75 and 48, we have to first simplify them. We can simplify them by the Prime Factorization method. Prime Factoring a number is to find the prime numbers which multiply together and make an original number.

Here we prime factorize both the numbers, and we get:
\[\sqrt {75} = \sqrt {5 \times 5 \times 3} \] and \[\sqrt {48} = \sqrt {2 \times 2 \times 2 \times 2 \times 3} \]
where 75 is having 5 and 3 as prime factors. The number 48 is having its prime factors as 2 and 3.When we simplify for \[\sqrt {75} \], we get:
\[ \Rightarrow \sqrt {75} = \sqrt {{5^2} \times 3} \]
Now, we will take out 5 from the square root, and we get:
\[ \Rightarrow \sqrt {75} = 5\sqrt 3 \]

When we simplify for \[\sqrt {48} \], we get:
\[ \Rightarrow \sqrt {48} = \sqrt {{2^2} \times {2^2} \times 3} \]
Now, we will take out both the 2’s from the square root and multiply them, and we get:
\[ \Rightarrow \sqrt {48} = 4\sqrt 3 \]
Now, according to the question, we will add both the square roots. So, we will add both the values of the square roots, and we get:
\[ \Rightarrow \sqrt {75} + \sqrt {48} = 5\sqrt 3 + 4\sqrt 3 \]
We can see the square root for both the terms is same, so we will just add 5 and 4, and we get:
\[ \therefore\sqrt {75} + \sqrt {48} = 9\sqrt 3 \]

Therefore, we get that (Square root of 75) + (Square root of 48) is \[9\sqrt 3 \].

Note: We should always keep in mind that when we add any numbers or values which contain square roots, we need to check whether the root part is the same for both the terms or not. If the root part is equal, then only the addition and subtraction actions are possible.