Section 1
Finding Roots
Decide whether each statement is true or false. If it is false, explain why.$$\sqrt{121}=11 \text { and }-11$$
Decide whether each statement is true or false. If it is false, explain why.$$\sqrt{81}=9$$
Decide whether each statement is true or false. If it is false, explain why.The square root of a negative number is a negative number.
Decide whether each statement is true or false. If it is false, explain why.The square root of a nonnegative number is always positive.
Find all square roots of each number.$$49$$
Find all square roots of each number.$$144$$
Find all square roots of each number.$$1$$
Find all square roots of each number.$$400$$
Find all square roots of each number.$$900$$
Find all square roots of each number.$$2500$$
Find all square roots of each number.$$\frac{4}{9}$$
Find all square roots of each number.$$\frac{36}{25}$$
Find all square roots of each number.$$\frac{1}{81}$$
Find all square roots of each number.$$\frac{1}{16}$$
Find all square roots of each number.$$0.25$$
Find all square roots of each number.$$0.01$$
Find each square root, if possible.$$\sqrt{49}$$
Find each square root, if possible.$$\sqrt{144}$$
Find each square root, if possible.$$\sqrt{1}$$
Find each square root, if possible.$$\sqrt{81}$$
Find each square root, if possible.$$\sqrt{169}$$
Find each square root, if possible.$$\sqrt{36}$$
Find each square root, if possible.$$\sqrt{-4}$$
Find each square root, if possible.$$\sqrt{-100}$$
Find each square root, if possible.$$\sqrt{\frac{81}{25}}$$
Find each square root, if possible.$$\sqrt{\frac{121}{4}}$$
Find each square root, if possible.$$-\sqrt{36}$$
Find each square root, if possible.$$-\sqrt{64}$$
Find each square root, if possible.$$-\sqrt{\frac{1}{121}}$$
Find each square root, if possible.$$-\sqrt{\frac{1}{100}}$$
Find each square root, if possible.$$\sqrt{0.04}$$
Find each square root, if possible.$$-\sqrt{0.36}$$
Approximate each square root to the nearest tenth and plot it on a number line.$$\sqrt{11}$$
Approximate each square root to the nearest tenth and plot it on a number line.$$\sqrt{2}$$
Approximate each square root to the nearest tenth and plot it on a number line.$$\sqrt{46}$$
Approximate each square root to the nearest tenth and plot it on a number line.$$\sqrt{22}$$
Approximate each square root to the nearest tenth and plot it on a number line.$$\sqrt{17}$$
Approximate each square root to the nearest tenth and plot it on a number line.$$\sqrt{69}$$
Approximate each square root to the nearest tenth and plot it on a number line.$$\sqrt{5}$$
Approximate each square root to the nearest tenth and plot it on a number line.$$\sqrt{35}$$
Approximate each square root to the nearest tenth and plot it on a number line.$$\sqrt{61}$$
Approximate each square root to the nearest tenth and plot it on a number line.$$\sqrt{8}$$
Decide whether each statement is true or false. If it is false, explain why.The cube root of a negative number is a negative number.
Decide whether each statement is true or false. If it is false, explain why.The even root of a negative number is a negative number.
Decide whether each statement is true or false. If it is false, explain why.Every nonnegative real number has two real, even roots.
Decide whether each statement is true or false. If it is false, explain why.Explain how to find $\sqrt[3]{64}$
Decide whether each statement is true or false. If it is false, explain why.Explain how to find $\sqrt[4]{16}$
Decide whether each statement is true or false. If it is false, explain why.Does $\sqrt[4]{-81}=-3 ?$ Why or why not?
Decide whether each statement is true or false. If it is false, explain why.Does $\sqrt[3]{-8}=-2 ?$ Why or why not?
Find each root, if possible.$$\sqrt[3]{8}$$
Find each root, if possible.$$\sqrt[3]{1}$$
Find each root, if possible.$$\sqrt[3]{125}$$
Find each root, if possible.$$\sqrt[3]{27}$$
Find each root, if possible.$$\sqrt[3]{-1}$$
Find each root, if possible.$$\sqrt[3]{-8}$$
Find each root, if possible.$$\sqrt[4]{81}$$
Find each root, if possible.$$\sqrt[4]{16}$$
Find each root, if possible.$$\sqrt[4]{-1}$$
Find each root, if possible.$$\sqrt[4]{-81}$$
Find each root, if possible.$$-\sqrt[4]{16}$$
Find each root, if possible.$$-\sqrt[4]{1}$$
Find each root, if possible.$$\sqrt[5]{-32}$$
Find each root, if possible.$$-\sqrt[6]{64}$$
Find each root, if possible.$$-\sqrt[3]{-27}$$
Find each root, if possible.$$-\sqrt[3]{-1000}$$
Find each root, if possible.$$\sqrt[6]{-64}$$
Find each root, if possible.$$\sqrt[3]{\frac{8}{125}}$$
Find each root, if possible.$$\sqrt[4]{\frac{81}{16}}$$
Find each root, if possible.$$\sqrt{60-11}$$
Find each root, if possible.$$\sqrt{100+21}$$
Find each root, if possible.$$\sqrt[3]{100+25}$$
Find each root, if possible.$$\sqrt[3]{9-36}$$
Find each root, if possible.$$\sqrt{1-9}$$
Find each root, if possible.$$\sqrt{25-36}$$
Find each root, if possible.$$\sqrt{5^{2}+12^{2}}$$
Find each root, if possible.$$\sqrt{3^{2}+4^{2}}$$
If $n$ is a positive, even integer and we are not certain that $a \geq 0,$ then we must use the absolute value symbol to evaluate $\sqrt[n]{a^{n}}$. That is, $\sqrt[n]{a^{n}}=|a|$. Why must we use the absolute value symbol?
If $n$ is a positive, odd integer, then $\sqrt[n]{a^{n}}=a$ for any value of $a$. Why don't we need to use the absolute value symbol?
Simplify.$$\sqrt{8^{2}}$$
Simplify.$$\sqrt{5^{2}}$$
Simplify.$$\sqrt{(-6)^{2}}$$
Simplify.$$\sqrt{(-11)^{2}}$$
Simplify.$$\sqrt{y^{2}}$$
Simplify.$$\sqrt{d^{2}}$$
Simplify.$$\sqrt{m^{2}}$$
Simplify.$$\sqrt{t^{2}}$$
Simplify.$$\sqrt[3]{5^{3}}$$
Simplify.$$\sqrt[3]{1^{3}}$$
Simplify.$$\sqrt[3]{(-4)^{3}}$$
Simplify.$$\sqrt[3]{(-3)^{3}}$$
Simplify.$$\sqrt[3]{z^{3}}$$
Simplify.$$\sqrt[5]{t^{5}}$$
Simplify.$$\sqrt[4]{h^{4}}$$
Simplify.$$\sqrt[5]{v^{5}}$$
Simplify.$$\sqrt[9]{p^{9}}$$
Simplify.$$\sqrt[6]{m^{6}}$$
Simplify.$$\sqrt{(x+7)^{2}}$$
Simplify.$$\sqrt{(a-9)^{2}}$$
Simplify.$$\sqrt[3]{(2 t-1)^{3}}$$
Simplify.$$\sqrt[5]{(6 r+7)^{5}}$$
Simplify.$$\sqrt[4]{(3 n+2)^{4}}$$
Simplify.$$\sqrt[3]{(x-6)^{3}}$$
Simplify.$$\sqrt[7]{(d-8)^{7}}$$
Simplify.$$\sqrt[6]{(4 y+3)^{6}}$$