Classify $$\left(\sqrt[]{5}+\frac{1}{5}\right)$$ as rational or irrational, and explain your reasoning.

Suppose an irrational + rational = rational, then irrational = rational – rational. This means irrational = rational, which is a contradiction. Thus the irrational number $$\sqrt[]{5}$$ plus the rational number $$\frac{1}{5}$$ equals the irrational number $$\left(\sqrt[]{5}+\frac{1}{5}\right)$$ .

Suppose an irrational + rational = rational, then irrational = rational – rational. This means that irrational = rational. Thus the irrational number $$\sqrt[]{5}$$ plus the rational number $$\frac{1}{5}$$ equals $$\left(\sqrt[]{5}+\frac{1}{5}\right)$$ , which is both rational and irrational .

Suppose an irrational + rational = rational, then irrational = rational – rational. This means irrational = rational, which is a contradiction. Thus the irrational number $$\sqrt[]{5}$$ plus the rational number $$\frac{1}{5}$$ equals the rational number $$\left(\sqrt[]{5}+\frac{1}{5}\right)$$ .

Suppose an irrational + rational = rational, then irrational = rational – rational. This means irrational = rational, which is a contradiction. Thus the irrational number $$\sqrt[]{5}$$ plus the rational number $$\frac{1}{5}$$ equals $$\left(\sqrt[]{5}+\frac{1}{5}\right)$$ , which is neither rational nor irrational .

Rational/irrational Numbers

Rational/Irrational Numbers

Authored by Raymee Burrell

Mathematics

8th Grade

CCSS covered

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CATEGORIZE QUESTION

3 mins • 6 pts

Sort all the rational and irrational numbers (when fully simplified):
$\pi,\ \ \ \ \ \ \ \ \ \ \ \ \ \frac{3}{10},\ \ \ \ \ \ \ \ \ \ 0.295,\ \ \ \ \ \ \ \ \ \ \sqrt{12},\ \ \ \ \ \ \ \ \ \ 0\overline{.5656},\ \ \ \ \ \ \ \ \ \ 7$

Groups:

(a) Rational

(b) Irrational

$0.\overline{5656}$

$\frac{3}{10}$

$0.295$

$\pi$

$\sqrt[]{12}$

$7$

Tags

CCSS.HSN.RN.B.3

MULTIPLE CHOICE QUESTION

30 sec • 2 pts

Determine if the simplified answer would be rational or irrational for. Hint: Use a calculator!
$\sqrt[]{5\ }+8$

Rational

Irrational

Tags

CCSS.HSN.RN.B.3

MULTIPLE CHOICE QUESTION

30 sec • 2 pts

Determine if the simplified answer would be rational or irrational for. Hint: Use a calculator!
$3\cdot14$

Rational

Irrational

Tags

CCSS.HSN.RN.B.3

MULTIPLE CHOICE QUESTION

30 sec • 2 pts

Determine if the simplified answer would be rational or irrational for. Hint: Use a calculator!
$\sqrt[]{4}\cdot\sqrt[]{4}$

Irrational

Rational

Tags

CCSS.HSN.RN.B.3

MULTIPLE CHOICE QUESTION

30 sec • 2 pts

Determine if the simplified answer would be rational or irrational for. Hint: Use a calculator!
$7-\ \sqrt[]{9}$

Rational

Irrational

MULTIPLE CHOICE QUESTION

30 sec • 3 pts

Simplify √72.
Select the answer that SHOWS the correct WORK!

√72 = √(36 * 2) = √36 * √2 = 6√2

√72 = √(49 * 2) = √49 * √2 = 7√2

√72 = √(25 * 3) = √25 * √3 = 5√3

√72 = √(64 * 1) = √64 * √1 = 8

Tags

CCSS.HSN.RN.A.2

CCSS.HSA.SSE.B.3

MULTIPLE CHOICE QUESTION

30 sec • 4 pts

Simplify $\sqrt{18x^5}$ .
Your answer must include a radical!

$3x^2\sqrt{2x}$

$6x^2\sqrt{x}$

$3x\sqrt{6x^3}$

$\sqrt{18x^5}$

Tags

CCSS.HSN.RN.A.2

MATH RESPONSE QUESTION

2 mins • 3 pts

What is the fully simplified form of $3\sqrt{5} \cdot 2\sqrt{15}$ ?
Your answer must include a radical!

$30\sqrt{3}$

Mathematical Equivalence

OFF

Tags

CCSS.HSN.RN.A.2

CCSS.HSN.RN.A.1

MULTIPLE CHOICE QUESTION

30 sec • 2 pts

Which of the following would be the simplified expression of $-4\sqrt{6} + 7\sqrt{6}$ ? Circle the correct answer.

$3\sqrt{12}$

$-3\sqrt{12}$

$3\sqrt{6}$

$-3\sqrt{6}$

$Cannot\ be\ simplified$

Tags

CCSS.HSN.RN.A.2

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the simplified form of $2\sqrt{3} - \sqrt{27}$ ?

$\sqrt{3}$

$-\sqrt{3}$

$3\sqrt{3}$

$-3\sqrt{3}$

Tags

CCSS.HSN.RN.A.2

CCSS.HSA.SSE.B.3

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Rational/Irrational Numbers

Sort all the rational and irrational numbers (when fully simplified): π, 310, 0.295, 12, 0.5656‾, 7\pi,\ \ \ \ \ \ \ \ \ \ \ \ \ \frac{3}{10},\ \ \ \ \ \ \ \ \ \ 0.295,\ \ \ \ \ \ \ \ \ \ \sqrt{12},\ \ \ \ \ \ \ \ \ \ 0\overline{.5656},\ \ \ \ \ \ \ \ \ \ 7π, 103​, 0.295, 12​, 0.5656, 7

Determine if the simplified answer would be rational or irrational for. Hint: Use a calculator! 5 +8\sqrt[]{5\ }+85 ​+8

Determine if the simplified answer would be rational or irrational for. Hint: Use a calculator! 3⋅143\cdot143⋅14

Determine if the simplified answer would be rational or irrational for. Hint: Use a calculator! 4⋅4\sqrt[]{4}\cdot\sqrt[]{4}4​⋅4​

Determine if the simplified answer would be rational or irrational for. Hint: Use a calculator! 7− 97-\ \sqrt[]{9}7− 9​

Simplify √72. Select the answer that SHOWS the correct WORK!

Simplify 18x5\sqrt{18x^5}18x5​ . Your answer must include a radical!

What is the fully simplified form of 35⋅2153\sqrt{5} \cdot 2\sqrt{15}35​⋅215​ ?Your answer must include a radical!

Which of the following would be the simplified expression of −46+76-4\sqrt{6} + 7\sqrt{6}−46​+76​ ? Circle the correct answer.

What is the simplified form of 23−272\sqrt{3} - \sqrt{27}23​−27​ ?

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Discover more resources for Mathematics

Sort all the rational and irrational numbers (when fully simplified):
$\pi,\ \ \ \ \ \ \ \ \ \ \ \ \ \frac{3}{10},\ \ \ \ \ \ \ \ \ \ 0.295,\ \ \ \ \ \ \ \ \ \ \sqrt{12},\ \ \ \ \ \ \ \ \ \ 0\overline{.5656},\ \ \ \ \ \ \ \ \ \ 7$

Determine if the simplified answer would be rational or irrational for. Hint: Use a calculator!
$\sqrt[]{5\ }+8$

Determine if the simplified answer would be rational or irrational for. Hint: Use a calculator!
$3\cdot14$

Determine if the simplified answer would be rational or irrational for. Hint: Use a calculator!
$\sqrt[]{4}\cdot\sqrt[]{4}$

Determine if the simplified answer would be rational or irrational for. Hint: Use a calculator!
$7-\ \sqrt[]{9}$

Simplify √72.
Select the answer that SHOWS the correct WORK!

Simplify $\sqrt{18x^5}$ .
Your answer must include a radical!

What is the fully simplified form of $3\sqrt{5} \cdot 2\sqrt{15}$ ?
Your answer must include a radical!

Which of the following would be the simplified expression of $-4\sqrt{6} + 7\sqrt{6}$ ? Circle the correct answer.

What is the simplified form of $2\sqrt{3} - \sqrt{27}$ ?