simplifying 169 to 1/2 power
- Thread starter mesiah
- Start date
Re: simplifying
\(\displaystyle 169^{\frac{1}{2}}=\sqrt{169}=???\)
Find two whole numbers which when multiplied together = 169.
2 X 84.5 = 169 >>> 84.5 not whole. Won't work.
3 X 56.333... = 169 >>> won't work. All multiples of 3 won't work.
4 X >>>Since 2 won't work no multiple of 2 will work so 4 won't work.
5 X 33.8 >>> 5 and all multiples of 5 won't work.
6 is multiple of both 2 and 3 so won't work.
7 X 24.14... >>> 7 and all multiples of 7 wont' work.
8 is multiple of 2
9 is multiple of 3
10 is multiple of both 2 and 5.
11 X 15.36... >>> 11 and ll multiples of 11 won't work.
12 is multiple of both 2 and 3.
13 X 13 = 169. Ahaa!
Therefore \(\displaystyle \sqrt{169}=\sqrt{13\cdot 13}=??\)
The rest is up to you.
100 to 3/2power = \(\displaystyle 100^{\frac{3}{2}}=100^{\frac{2}{2}}\cdot 100^{\frac{1}{2}}=???\)
\(\displaystyle 169^{\frac{1}{2}}=\sqrt{169}=???\)
Find two whole numbers which when multiplied together = 169.
2 X 84.5 = 169 >>> 84.5 not whole. Won't work.
3 X 56.333... = 169 >>> won't work. All multiples of 3 won't work.
4 X >>>Since 2 won't work no multiple of 2 will work so 4 won't work.
5 X 33.8 >>> 5 and all multiples of 5 won't work.
6 is multiple of both 2 and 3 so won't work.
7 X 24.14... >>> 7 and all multiples of 7 wont' work.
8 is multiple of 2
9 is multiple of 3
10 is multiple of both 2 and 5.
11 X 15.36... >>> 11 and ll multiples of 11 won't work.
12 is multiple of both 2 and 3.
13 X 13 = 169. Ahaa!
Therefore \(\displaystyle \sqrt{169}=\sqrt{13\cdot 13}=??\)
The rest is up to you.
100 to 3/2power = \(\displaystyle 100^{\frac{3}{2}}=100^{\frac{2}{2}}\cdot 100^{\frac{1}{2}}=???\)
Re: simplifying
\(\displaystyle x^\frac{a}{b} = \sqrt{x^a}\)
Therefore \(\displaystyle 169^\frac{1}{2}=\sqrt[2]{169^1}=13\)
You don't usually use the index of 2. It's understood to be 2 without explicitly stating it. I just did that to illustrate the rule.
\(\displaystyle x^\frac{a}{b} = \sqrt{x^a}\)
Therefore \(\displaystyle 169^\frac{1}{2}=\sqrt[2]{169^1}=13\)
You don't usually use the index of 2. It's understood to be 2 without explicitly stating it. I just did that to illustrate the rule.
- Joined
- Feb 4, 2004
- Messages
- 16,582
mesiah said:
galactus said:
Erm... They were supposed to have covered exponents before assigning this sort of exercise. :shock:mesiah said:
To learn what fractional exponents are, and how they relate to radicals, try some online lessons to replace what your classroom lectures and your textbook skipped:
. . . . .Google results for "fractional exponent radical"
Have fun!
Eliz.