4. Evaluate Square Roots and Cube Roots
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Recall that a square has four equal sides. The volume of a cube is equal to the product of its three side lengths.
If the edge length of the block appears to be smaller than of equal to the edge length of the hole, then the block will fit in the hole.
See solution.
No, see solution.
We consider a toy which has various shaped objects that a child can push through matching holes. We will consider a square hole and a cube-shaped block. We know the area of the square hole, so we can find its edge length.
| Which edge length? | Can it be found? |
|---|---|
| Square hole | Yes |
The block we consider is cube-shaped and we know its volume of 64 cubic centimeters. Therefore, it enables us to obtain edge length of the block.
| Which edge length? | Can it be found? |
|---|---|
| Square hole | Yes |
| Cube-shaped block | Yes |
A= 8
Rearrange equation
sqrt(a^2)=a
We also know the volume of the cube-shaped block of 64 cubic centimeters. This enables us to calculate the edge length of the block. Recall that three side measurements of a cube — the length, the width, and the height — all happen to be the same. This time let's call the side length l.
sqrt(LHS)=sqrt(RHS)
Split into factors
a* a* a=a^3
sqrt(a^3)=a
sqrt(LHS)
Split into factors
a* a=a^2
sqrt(a^2)=a