Question

Part A: Use the properties of exponents to explain why 64 raised to the power of 1 over 2 is called the square root of 64.

Part B: The length of a rectangle is 7 units and its width is square root of 7 unit. Is the area of the rectangle rational or irrational?

Answer 1

hint: \(x^a\cdot x^b = x^{a+b}\)

Answer 2

for part A.

Answer 3

okay so how would i put the answer

Answer 4

use the property...

Answer 5

if a = 1/2 and b = 1/2 then what's \(\huge{64^{\frac{1}{2}}\cdot64^{\frac{1}{2}}}\)

Answer 6

is it becouse 8*8 = 64 and 64 1/2 is square root of 64

Answer 7

\[64^{\frac{1}{2}}\cdot64^{\frac{1}{2}}=64^1\] so what times itself = 64?

\[\sqrt{64}\cdot\sqrt{64} = 64\Rightarrow \sqrt{64}=64^{\frac{1}{2}}\]

Answer 8

also\[\left( 64^{\frac{1}{2}} \right)^2 =64^{\frac{1}{2}\cdot2}=64^{1} \Rightarrow 64^{\frac{1}{2}}=\sqrt{64}\]

Answer 9

8

Answer 10

just using a different property of exponents

Answer 11

it's not about \(64^{\frac{1}{2}}=8\) but \(x^{\frac{1}{2}}=\sqrt{x}\)

Answer 12

oh okay i get it now!

Answer 13

good!

Answer 14

can u help me with part b

Answer 15

what's the area?

Answer 16

would it be 14

Answer 17

length times width

Answer 18

42

Answer 19

what's the length?

Answer 20

7

Answer 21

and what's the width?

Answer 22

7 squared

Answer 23

square root of 7

Answer 24

there you go. so multiply them \[7\cdot \sqrt{7}=?\]

Answer 25

18.2?

Answer 26

\[7\sqrt{7}\]

Answer 27

is that rational or irrational?

Answer 28

rational

Answer 29

really? is \(\sqrt{7}\) rational?

Answer 30

irrational? 0_o

i suck at math.

Answer 31

don't say that! you can say you're working to improve. keep it positive!

rational simply means that a number can be expressed as a fraction.

\(\sqrt{7}\) cannot be expressed as a fraction. it can be approximated with a fraction but there is no fraction involving only integers which equals \(\sqrt{7}\).

Answer 32

fraction = ratio of integers

Answer 33

or actually, rational number means "ratio of integers."

Answer 34

:O thanks! u helped a lot!

Answer 35

you're welcome!