Question

Compare. Write , or =.​

Answer 1

• You can add or subtract (and divide if positive) same value to both sides of an inequality, it doesn't change the balance but makes it easier to decide.

#1 <

• √3 + 2 vs √3 + 3
• 2 < 3

#2 >

• √11 + 15 vs √8 + 15
• √11 > √8

#3 <

• √6 + 5 vs 6 + √5
• √6 - √5 vs 6 - 5 = (√6 + √5)(√6-√5)
• 1 < √6 + √5

#4 <

• √9 + 3 vs 9 + √3
• 3 + 3 = 6 < 9 + √3
• This can be solved similarly to #3 too

#5 >

• √17 - 3 vs -2 + √5
• √17 - 3 > 4 - 3 = 1 and √5 - 2 < 3 -2 = 1
• Left side is greater than 1, right side is smaller than 1

#6 <

• 10 - √8 vs 12 - √2
• 10 - 12 = -2 < √8 - √2 > 0

#7 >

• √7 + 2 vs √10 - 1
• 2 + 1 = 3 > √10 - √7

#8 >

• √17 + 3 vs 3 + √11
• √17 > √ 11