3.5 Irrational Numbers

Determine which of the following are perfect squares.

1. 45
2. 81
3. $\frac{9}{28}$
4. $\frac{144}{400}$

Identify which of the following numbers are irrational.

1. $\sqrt{35}$
2. $0. \bar{15}$
3. $\sqrt{121}$
4. $4 \pi$

Simplify the irrational number $\sqrt{180}$ and express in lowest terms. Identify the rational and irrational parts.

Simplify the irrational number $\sqrt{330}$ and express in lowest terms. Identify the rational and irrational parts.

Simplify the irrational number $\sqrt{2,548}$ and express in lowest terms. Identify the rational and irrational parts.

If possible, subtract the following irrational numbers without using a calculator. If this is not possible, state why.

If possible, add the following irrational numbers without using a calculator. If this is not possible, state why.

$35 \pi + 17 \pi$

If possible, subtract the following irrational numbers without using a calculator. If this is not possible, state why.

$19 \sqrt{3} - 5.6 \sqrt{7}$

Perform the following operations without a calculator. Simplify if possible.

1. $3 \sqrt{15} \div \left(8 \sqrt{3}\right)$
2. $14.7 \sqrt{135} \div \left(3 \sqrt{5}\right)$.

Perform the following operations without a calculator. Simplify if possible.

1. $\left(19 \sqrt{3}\right) \times \left(5.6 \sqrt{12}\right)$
2. $13 \pi \times 8 \pi$

Rationalize the denominator of the following:

1. $\frac{5}{\sqrt{7}}$
2. $\frac{3 \sqrt{6}}{2 \sqrt{10}}$

Rationalize the denominator of $\frac{4}{6 + \sqrt{10}}$.