SOLUTION: Perform the indicated multiplication. Then simplify each radical expression. 1. square root of 13 TIMES square root of 5 2. square root of 7(2 square root of 3 + 3 square roo

Algebra ->  Square-cubic-other-roots -> SOLUTION: Perform the indicated multiplication. Then simplify each radical expression. 1. square root of 13 TIMES square root of 5 2. square root of 7(2 square root of 3 + 3 square roo      Log On


   

Question 118064: Perform the indicated multiplication. Then simplify each radical expression.
1. square root of 13 TIMES square root of 5
2. square root of 7(2 square root of 3 + 3 square root of 7)

Found 2 solutions by jim_thompson5910, ilana:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2813%29%2Asqrt%285%29 Start with the given expression

sqrt%2813%2A5%29 Combine the roots using the identity sqrt%28x%29%2Asqrt%28y%29=sqrt%28x%2Ay%29


sqrt%2865%29 Multiply 13 and 5 to get 65


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sqrt%287%29%282%2Asqrt%283%29+%2B+3%2Asqrt%287%29%29 Start with the given expression


2%2Asqrt%283%29%2Asqrt%287%29+%2B+3%2Asqrt%287%29%2Asqrt%287%29 Distribute


2%2Asqrt%283%2A7%29+%2B+3%2Asqrt%287%2A7%29 Combine the roots using the identity sqrt%28x%29%2Asqrt%28y%29=sqrt%28x%2Ay%29


2%2Asqrt%2821%29+%2B+3%2Asqrt%2849%29 Multiply


2%2Asqrt%2821%29+%2B+3%2A7 Take the square root of 49 to get 7


2%2Asqrt%2821%29+%2B+21 Multiply

Answer by ilana(307) About Me  (Show Source):
You can put this solution on YOUR website!
In general, sqrt(a)*sqrt(b)=sqrt(a*b).
So for the first problem, simply multiply the 13 and 5 to get sqrt(65). Now you need to see if this can be simplified by dividing by a perfect square. Is it divisible by 4, 9, 16, 25, 36, 49, 64? Nope. So sqrt(65) is simplified.
The second part is more complicated because you need to distribute. This works the same as something like x(3x+5x). You multiply the outside by both parts. So sqrt7(2sqrt3+3sqrt7)=2sqrt21+3sqrt49. Now simplify: 2sqrt21+3*7 = 2sqrt21 + 21