Question

Drag the tiles to the correct boxes to complete the pairs.

Match each radical equation with its solution.

Answer 1

• x=5 →
  `√((x-1)^3)=8`

• x=19 →
  `\sqrt[4]{(x-3)^5}=32`

• x=29 →
  `√((x-4)^3)=125`

• x=6 →
  `\sqrt[3]{(x+2)^4}=16`

Explanation:

First tile:

`√((x-1)^3)=8`

When we put x=5 we obtain:

`√((5-1)^3)=8\\\\√(4^3)=8\\\\√(64)=8\\\\√(8^2)=8\\\\8=8`

Hence, the first tile must be dragged to x=5

Second tile:

`\sqrt[4]{(x-3)^5}=32\\\\(x-3)^5=(32)^4\\\\(x-3)^5=(2^5)^4`

Now when x=19

we have:

`(19-3)^5=(2^5)^4\\\\(16)^5=2^(20)\\\\(2^4)^5=2^(20)\\\\2^(20)=2^(20)`

( Since:

`(a^m)^n=a^(mn)` )

Third tile:

`√((x-4)^3)=125\\\\(x-4)^3=(125)^2\\\\Since\ on\ squaring\ both\ side\ of\ the\ equation\\\\(x-4)^3=(5^3)^2\\\\(x-4)^3=5^6`

when x=29 we have:

`(29-4)^3=5^6\\\\(25)^3=5^6\\\\(5^2)^3=5^6\\\\5^6=5^6`

Fourth tile:

`\sqrt[3]{(x+2)^4}=16\\\\On\ cubing\ both\ side\ of\ the\ equation\ we\ get:\\\\(x+2)^4=(16)^3\\\\(x+2)^4=(2^4)^3\\\\(x+2)^4=2^(12)`

when x=6 we have:

`8^4=2^(12)\\\\(2^3)^4=2^(12)\\\\2^(12)=2^(12)`