Pythagorean theorem and irrational numbers

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A square has an area of 225 square units. How long is its side?
$\sqrt{ 37 }$ lies between two consecutive whole numbers. What is the smaller one?
A cube has a volume of 343 cubic units. How long is each edge?
Which number is irrational?
1. $\sqrt{ 2 }$
2. $\sqrt{ 4 }$
3. $0.\overline{ 1 }$
Which number is irrational?
1. $\sqrt{ 10 }$
2. $\sqrt{ 16 }$
3. $0.\overline{ 3 }$
Which number is irrational?
1. $\sqrt{ 37 }$
2. $\sqrt{ 49 }$
3. $0.\overline{ 6 }$
Which number is irrational?
1. $\sqrt{ 26 }$
2. $\sqrt{ 36 }$
3. $0.\overline{ 5 }$
Which number is irrational?
1. $\sqrt{ 5 }$
2. $\sqrt{ 9 }$
3. $0.\overline{ 2 }$
Which number is irrational?
1. $\sqrt{ 17 }$
2. $\sqrt{ 25 }$
3. $0.\overline{ 4 }$
Which number is irrational?
1. $\sqrt{ 65 }$
2. $\sqrt{ 81 }$
3. $0.\overline{ 8 }$
Which number is irrational?
1. $\sqrt{ 50 }$
2. $\sqrt{ 64 }$
3. $0.\overline{ 7 }$
Which number is irrational?
1. $\sqrt{ 82 }$
2. $\sqrt{ 100 }$
3. $0.\overline{ 9 }$
Write $0.\overline{ 1 }$ (the digit 1 repeating forever) as a fraction.
Write $0.\overline{ 48 }$ (the digits 48 repeating forever) as a fraction.
A right triangle has legs 10 and 24. How long is the hypotenuse?
A right triangle has hypotenuse 15 and one leg 9. How long is the other leg?
A right triangle has legs 2 and 4. Find the exact length of the hypotenuse.
Is a triangle with sides 3, 4 and 5 a right triangle?
1. Yes: the squares of the two shorter sides add up to the square of the longest
2. No: the sides are not consecutive whole numbers
3. You cannot tell without measuring an angle
Is a triangle with sides 9, 12 and 15 a right triangle?
1. Yes: the squares of the two shorter sides add up to the square of the longest
2. No: the sides are not consecutive whole numbers
3. You cannot tell without measuring an angle
Is a triangle with sides 15, 20 and 25 a right triangle?
1. Yes: the squares of the two shorter sides add up to the square of the longest
2. No: the sides are not consecutive whole numbers
3. You cannot tell without measuring an angle
Is a triangle with sides 12, 16 and 20 a right triangle?
1. Yes: the squares of the two shorter sides add up to the square of the longest
2. No: the sides are not consecutive whole numbers
3. You cannot tell without measuring an angle
Is a triangle with sides 6, 8 and 10 a right triangle?
1. Yes: the squares of the two shorter sides add up to the square of the longest
2. No: the sides are not consecutive whole numbers
3. You cannot tell without measuring an angle
Is a triangle with sides 7, 8 and 9 a right triangle?
1. No: 49 + 64 is not 81
2. Yes: like 3, 4, 5, the sides are consecutive
3. You cannot tell without measuring an angle
Is a triangle with sides 6, 7 and 8 a right triangle?
1. No: 36 + 49 is not 64
2. Yes: like 3, 4, 5, the sides are consecutive
3. You cannot tell without measuring an angle
Is a triangle with sides 9, 10 and 11 a right triangle?
1. No: 81 + 100 is not 121
2. Yes: like 3, 4, 5, the sides are consecutive
3. You cannot tell without measuring an angle
Is a triangle with sides 5, 6 and 7 a right triangle?
1. No: 25 + 36 is not 49
2. Yes: like 3, 4, 5, the sides are consecutive
3. You cannot tell without measuring an angle
Is a triangle with sides 8, 9 and 10 a right triangle?
1. No: 64 + 81 is not 100
2. Yes: like 3, 4, 5, the sides are consecutive
3. You cannot tell without measuring an angle
Is a triangle with sides 4, 5 and 6 a right triangle?
1. No: 16 + 25 is not 36
2. Yes: like 3, 4, 5, the sides are consecutive
3. You cannot tell without measuring an angle
A 13 ft ladder leans against a wall and reaches 12 ft up. How far is its foot from the wall?
Find the distance between $(-1, -3)$ and $(2, 1)$ .
Tap the midpoint of the segment from $(-6, -5)$ to $(-4, -1)$ .
Find the exact distance between $(0, -2)$ and $(1, -4)$ .

Answers

$15$
$6$
$7$
$\sqrt{ 2 }$
$\frac{1}{9}$
$\frac{16}{33}$
$26$
$12$
$2 \sqrt{5}$
Yes: the squares of the two shorter sides add up to the square of the longest
No: 49 + 64 is not 81
$5$
$5$
$(-5, -3)$
$\sqrt{5}$