Question

How do you simplify $ \sqrt{35}\times \sqrt{15} $ ?

Answer 1

Hint: We can apply the formula $ {{a}^{m}}{{b}^{m}}={{\left( ab \right)}^{m}} $ to solve the problem where a is equal to 35 , b is 15 and m is equal to 0.5 . $ \sqrt{35}\times \sqrt{15} $ will be equal to square root of $ 35\times 15 $ then we can write $ 35\times 15 $ as product of its prime factors and solve the problem.

Complete step by step answer:
To solve $ \sqrt{35}\times \sqrt{15} $ we can apply the exponential property which is $ {{a}^{m}}{{b}^{m}}={{\left( ab \right)}^{m}} $ where m is equal to 0.5
So we can write $ \sqrt{35}\times \sqrt{15} $ as $ \sqrt{35\times 15} $ which is equal to $ \sqrt{525} $
Now let’s write 525 as product of its prime factor
So $ 525=5\times 5\times 3\times 7 $
We can write $ \sqrt{525}=\sqrt{5\times 5\times 3\times 7} $
Now separating square root of $ 5\times 5 $ , square root of 3 and 7
  $ \sqrt{525}=\sqrt{5\times 5}\times \sqrt{7\times 3} $ …eq1
  $ \sqrt{5\times 5} $ is equal to 5 and $ \sqrt{7\times 3} $ is equal to $ \sqrt{21} $ replacing in eq1
  $ \sqrt{525}=5\sqrt{21} $
So the value of $ \sqrt{35}\times \sqrt{15} $ is equal to $ 5\sqrt{21} $.

Note:
Another method we can try is to solve each term individually and then multiply.
So solving $ \sqrt{35} $ we can write 35 as product of its prime factors
So $ \sqrt{35}=\sqrt{5\times 7} $
By apply the exponential formula $ {{a}^{m}}{{b}^{m}}={{\left( ab \right)}^{m}} $ we can write
  $ \sqrt{35}=\sqrt{5}\times \sqrt{7} $