Question

What is the exact value for the expression square root of 171 - square root of 19 + square root of 76 ? Simplify if possible. plzz help

Answer 1

171, 19 and 76 all have a GCF of 19,
171/19 = 9
19/19 = 1
76/19 = 4
Now we can conclude:
9 x 19 = 171
1 x 19 = 19
4 x 19 = 76
Now we know\[\sqrt{ab} = \sqrt{a} \times \sqrt{b}\]
So
\[\sqrt{(9)\times19}=171\]
\[\sqrt{(1)\times19}=19\]
\[\sqrt{(4)\times19}=76\]
Now seperate the square root, so it is sqrt(a) x sqrt(b)
Take the square root of the perfect square...(in brackets)
so we get
\[3\sqrt{19}\]
\[1\sqrt{19}\]
\[2\sqrt{19}\]
Add/Subtract with the appropriate sign...
We get \[4\sqrt{19}\] as a result