GCSE Powers and roots Practice Questions

Recall what the power means

A power tells you how many times to multiply the base by itself, so this means $7$ multiplied $2$ times.

Write it out in full

Writing every factor out makes the repeated multiplication clear.

Multiply the final factor

Multiply $7$ by the last $7$, giving $49$.

Recall what the power means

A power tells you how many times to multiply the base by itself, so this means $6$ multiplied $2$ times.

Write it out in full

Writing every factor out makes the repeated multiplication clear.

Multiply the final factor

Multiply $6$ by the last $6$, giving $36$.

Picture it as a square array

A square number is the number of dots in a square grid; a $6$ by $6$ grid holds $36$ dots.

Recall what the power means

A power tells you how many times to multiply the base by itself, so this means $11$ multiplied $2$ times.

Write it out in full

Writing every factor out makes the repeated multiplication clear.

Multiply the final factor

Multiply $11$ by the last $11$, giving $121$.

List the powers as a check

Listing each power in order confirms none were missed.

State the final answer

So the value of the power is $121$.

Underline the final answer

Write the answer on its own line so it is clear and easy to mark.

Recall square numbers

Square numbers come from squaring whole numbers.

Test $16$

$16$ is a square number.

Test $20$

$20$ is between $16$ and $25$, so not square.

Test $25$

$25$ is a square number.

Test $30$

$30$ is between $25$ and $36$, so not square.

Test $36$

$36$ is a square number.

Collect the squares

Gather the ones that passed.

State the answer

These are the square numbers in the list.

Check

They are $4^2$, $5^2$ and $6^2$ respectively.

Underline the final answer

Write the answer on its own line so it is clear and easy to mark.

Link tiles to a square array

A square arrangement means side x side tiles.

Find the side

Take the square root of $196$.

Try a number just below

Testing $13$ gives $169$, which is too small.

Try the next number

Testing $14$ gives exactly $196$, so this is the root.

Verify by multiplying back

Check the root by squaring it back to $196$.

Split the second number by place value

Break $14$ into $10 + 4$ so we can multiply in easy parts.

Multiply the tens part

First multiply by the $10$.

Multiply the units part

Then multiply by the $4$.

Add the two parts

Add the partial products to get $196$.

State part (a)

Each side has $14$ tiles.

Set up the border count

Four sides of $14$ tiles each is a first estimate.

Multiply

That gives $56$.

Adjust for corners

The $4$ corner tiles were counted twice, so subtract $4$.

State part (b)

There are $52$ tiles on the border.

Sense check

Total tiles minus the $12$x1$2$ interior also gives $52$ border tiles.

Final answer

The requested final answer is the border count, $52$.