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7. Fill in <, > or =

a. √36 □ √25

b. √81 □ ∛27

c. √9 □ √16

d. √81 □ 32

e. 32 □ √36

f. 42 □ √25

Answer :

To solve these comparison problems, we need to evaluate the square roots and cube roots where necessary and then compare the resulting values.

  1. √36 □ √25

    • Evaluate each square root:
      • [tex]\sqrt{36} = 6[/tex]
      • [tex]\sqrt{25} = 5[/tex]
    • Compare:
      • Since 6 is greater than 5, we write:
        [tex]\sqrt{36} > \sqrt{25}[/tex]

  2. √81 □ ∛27

    • Evaluate each root:
      • [tex]\sqrt{81} = 9[/tex]
      • [tex]\sqrt[3]{27} = 3[/tex]
    • Compare:
      • Since 9 is greater than 3, we write:
        [tex]\sqrt{81} > \sqrt[3]{27}[/tex]

  3. √9 □ √16

    • Evaluate each square root:
      • [tex]\sqrt{9} = 3[/tex]
      • [tex]\sqrt{16} = 4[/tex]
    • Compare:
      • Since 3 is less than 4, we write:
        [tex]\sqrt{9} < \sqrt{16}[/tex]

  4. √81 □ 32

    • Evaluate the square root:
      • [tex]\sqrt{81} = 9[/tex]
    • Compare:
      • Since 9 is less than 32, we write:
        [tex]\sqrt{81} < 32[/tex]

  5. 32 □ √36

    • Evaluate the square root:
      • [tex]\sqrt{36} = 6[/tex]
    • Compare:
      • Since 32 is greater than 6, we write:
        [tex]32 > \sqrt{36}[/tex]

  6. 42 □ √25

    • Evaluate the square root:
      • [tex]\sqrt{25} = 5[/tex]
    • Compare:
      • Since 42 is greater than 5, we write:
        [tex]42 > \sqrt{25}[/tex]

For each part, we evaluated the necessary square or cube root and compared the numerical values to fill in the appropriate inequality sign ([tex]<[/tex], [tex]>[/tex], or [tex]=[/tex]).

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