Math Problem Statement

Which of the following are not rational square roots? Select all that apply. The weight of the blue whale is how many times as great as the weight of the giraffe? Quantity A is how many times as great as Quantity B? A mosquito is 4 x 10^-3 meters long, and a ladybug is 1 x 10^-2 meters long. How many meters longer is the ladybug than the mosquito?

Solution

Let's go through the questions in the image one by one:

Question 1

Which of the following are not rational square roots? Select all that apply.

  • A: 45\sqrt{45}
  • B: 121\sqrt{121}
  • C: 25\sqrt{25}
  • D: 27\sqrt{27}

Solution:

  • 45\sqrt{45} is irrational because 45 is not a perfect square.
  • 121=11\sqrt{121} = 11 is rational because 121 is a perfect square.
  • 25=5\sqrt{25} = 5 is rational because 25 is a perfect square.
  • 27\sqrt{27} is irrational because 27 is not a perfect square.

So, the irrational square roots are 45\sqrt{45} and 27\sqrt{27}.

Question 7

The weight of the blue whale is how many times as great as the weight of the giraffe?

  • Giraffe: 3×1033 \times 10^3 pounds
  • Blue Whale: 3×1053 \times 10^5 pounds

Solution: Ratio=3×1053×103=102=100\text{Ratio} = \frac{3 \times 10^5}{3 \times 10^3} = 10^2 = 100

So, the weight of the blue whale is 100 times the weight of the giraffe. The correct answer is (a) 100 times.

Question 8

Quantity A is how many times as great as Quantity B?

  • Quantity A: 6×1086 \times 10^8
  • Quantity B: 4×1054 \times 10^5

Solution: Ratio=6×1084×105=64×1085=1.5×103=1500\text{Ratio} = \frac{6 \times 10^8}{4 \times 10^5} = \frac{6}{4} \times 10^{8-5} = 1.5 \times 10^3 = 1500

So, Quantity A is 1500 times as great as Quantity B. The correct answer is (c) 1500 times.

Question 9

A mosquito is 4×1034 \times 10^{-3} meters long, and a ladybug is 1×1021 \times 10^{-2} meters long. How many meters longer is the ladybug than the mosquito?

Solution: Difference=1×1024×103=10×1034×103=6×103\text{Difference} = 1 \times 10^{-2} - 4 \times 10^{-3} = 10 \times 10^{-3} - 4 \times 10^{-3} = 6 \times 10^{-3}

So, the ladybug is 6×1036 \times 10^{-3} meters longer than the mosquito. The correct answer is (a) 6×1036 \times 10^{-3} meters.

Do you want more details or have any questions about these solutions?

Here are five relative questions to expand your understanding:

  1. What makes a number's square root rational or irrational?
  2. How do you convert scientific notation to standard form?
  3. What is the difference between a ratio and a fraction?
  4. How can you simplify expressions involving powers of ten?
  5. Why is it important to understand the magnitude of numbers in scientific notation?

Tip: When dealing with scientific notation, always ensure that you handle the powers of ten correctly, as they play a crucial role in comparing magnitudes.

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Math Problem Analysis

Mathematical Concepts

Square Roots
Scientific Notation
Ratios
Subtraction of Decimals in Scientific Notation

Formulas

Square root concept
Ratio = A / B
Subtraction of numbers in scientific notation

Theorems

Properties of Rational and Irrational Numbers

Suitable Grade Level

Grades 6-8