Answer:
The answer is [tex]3^{7}\sqrt{3}[/tex] ⇒ answer (d)
Step-by-step explanation:
* How to simplify the square root
- The square is even root ⇒ because 2 is an even number
- We can'f find square root for negative number,
- we can change the square root by rational exponent 1/2
* Lets look to our problem
- We have √(3^15)
- That means √(3^14 × 3)
- Lets change the square root to √3 to (3)^1/2
∵ [tex]\sqrt{3^{15}}=\sqrt{3^{14}(3)}=(3^{14})^{\frac{1}{2}}(3)^{\frac{1}{2}}[/tex]
∵ 14 × 1/2 = 7
∵ 3^1/2 = √3
∴ [tex]3^{7}(3^{\frac{1}{2}})=3^{7}\sqrt{3}[/tex]
∴ The answer is (d)
