Part 1
Without a calculator, determine what two consecutive integers the following numbers are between? How do you know? Justify your reasoning.
a) \(\sqrt{8}\)
b) \(\sqrt{32}\)
c) \(\sqrt[3]{20}\)
d) \(\sqrt[3]{60}\)
Part 2
Can you simplify the following expressions? Yes or no. Explain why or why not.
a) \(3x+7x\)
b) \(3y+3x\)
c) \(3x^2+7x\)
d) \(3\sqrt{x}+7\sqrt{x}\)
e) \(3x\sqrt{x}+7\sqrt{x}\)
f) \(3\sqrt{7xy}+7\sqrt{x}\)
g) \(3\sqrt{xy}+7x\sqrt{y}\)
h) \(3x^2\sqrt{5xyz^2}+7x^2\sqrt{5xyz^2}\)
Part 3
Simplify the following. Look for patterns as you work.
a) \(\sqrt{25}\cdot\sqrt{49}\)
b) \(\sqrt[3]{8}\cdot\sqrt[3]{27}\)
c) \(\sqrt{4\cdot9}\)
d) \(\sqrt[3]{8\cdot64}\)
e) \(\sqrt{32\cdot2}\)
f) \(\sqrt{3\cdot9}\)
g) \(\sqrt{\frac{32}{2}}\)
h) \(\sqrt[3]{\frac{54}{2}}\)
i) \(7x+8x\)
j) \(\sqrt{x}+5\sqrt{x}\)
k) \(5\sqrt[3]{x}+4\sqrt[3]{x}\)
Without a calculator, determine what two consecutive integers the following numbers are between? How do you know? Justify your reasoning.
a) \(\sqrt{8}\)
b) \(\sqrt{32}\)
c) \(\sqrt[3]{20}\)
d) \(\sqrt[3]{60}\)
Part 2
Can you simplify the following expressions? Yes or no. Explain why or why not.
a) \(3x+7x\)
b) \(3y+3x\)
c) \(3x^2+7x\)
d) \(3\sqrt{x}+7\sqrt{x}\)
e) \(3x\sqrt{x}+7\sqrt{x}\)
f) \(3\sqrt{7xy}+7\sqrt{x}\)
g) \(3\sqrt{xy}+7x\sqrt{y}\)
h) \(3x^2\sqrt{5xyz^2}+7x^2\sqrt{5xyz^2}\)
Part 3
Simplify the following. Look for patterns as you work.
a) \(\sqrt{25}\cdot\sqrt{49}\)
b) \(\sqrt[3]{8}\cdot\sqrt[3]{27}\)
c) \(\sqrt{4\cdot9}\)
d) \(\sqrt[3]{8\cdot64}\)
e) \(\sqrt{32\cdot2}\)
f) \(\sqrt{3\cdot9}\)
g) \(\sqrt{\frac{32}{2}}\)
h) \(\sqrt[3]{\frac{54}{2}}\)
i) \(7x+8x\)
j) \(\sqrt{x}+5\sqrt{x}\)
k) \(5\sqrt[3]{x}+4\sqrt[3]{x}\)