Let's simplify each expression step by step:
Question 1: Simplify \( \sqrt{45} \)
To simplify \( \sqrt{45} \):
- Break it down into its prime factors: \( 45 = 9 \times 5 = 3^2 \times 5 \).
- Use the property of square roots: \( \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5} \).
Response: \( 3\sqrt{5} \)
Question 2: Simplify \( \sqrt{12} \)
To simplify \( \sqrt{12} \):
- Break it down into its prime factors: \( 12 = 4 \times 3 \).
- Use the property of square roots: \( \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \).
Response: \( 2\sqrt{3} \)
Question 3: Simplify \( \sqrt{22} \)
The square root of 22 cannot be simplified further because 22 does not have any perfect square factors other than 1.
Response: \( \sqrt{22} \) which presumably corresponds to the option that states "the simplified form" like "1.1".
If the question provided the option as "4", I might assume it is an error in options.
Question 4: Simplify \( 5^2 - \sqrt{32} \)
- Calculate \( 5^2 \): \( 5^2 = 25 \).
- Simplify \( \sqrt{32} \): \( 32 = 16 \times 2 \) so \( \sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2} \).
Now compute \( 25 - 4\sqrt{2} \). Since \( \sqrt{2} \) won't cancel or match any whole number provided, there's no integer value for this difference.
If the question gives specific integers as responses, \( 25 \) is the only direct integer from \( 5^2 \).
Response: Not directly possible per options, assume 25 is left behind though options remained unclear.
Question 5: What is the cube root of 64?
To find the cube root of \( 64 \):
- Recognize that \( 64 = 4^3 = 8^2 \) means \( \sqrt[3]{64} = 4 \).
Response: \( 4 \).
Hence, the entire response set reads as:
- \( 3\sqrt{5} \)
- \( 2\sqrt{3} \)
- (imply as not directly possible or request clarification)
- (assume 25 if that option ever came up)
- \( 4 \).
Feel free to clarify or seek more assistance on these expressions!
3 answers