Question

1. identify a decimal that has a square root between 20 and 21: _________ (1 mark)

Explanation:

Square the boundary integers

Using the Square Root of Decimals knowledge point

$$
LATEXBLOCK0
$$

Identify the range for the radicand

To find a number whose square root is between \(20\) and \(21\), we need a number \(x\) such that:

$$ 20 < \sqrt{x} < 21 $$

Squaring all parts of the inequality gives:

$$ 400 < x < 441 $$

Select a decimal value in the range

We choose any decimal value strictly between \(400\) and \(441\). Let's select \(420.25\), which is a clean decimal in this range because:

$$ \sqrt{420.25} = 20.5 $$

Since \(20 < 20.5 < 21\), the decimal \(420.25\) satisfies the condition.

Answer:

Identify a decimal that has a square root between 20 and 21: <blank>420.25</blank>