Respuesta :
Answer:
The square root of a positive number greater than 1 is less than the number.
The square root of a positive number less than 1 is between 0 and 1
Step-by-step explanation:
The statements 1 and 5 are true based on the properties of square root.
What is square root?
The square root of any number is equal to a number, which when multiplied with the same number gives the original number. When a number multiplies itself, the product that is obtained is known as the square number. The number is the square root.
For the given situation,
Based on the properties of square root, some statements are there. We need to check which statements are correct.
Statement 1:
The square root of a positive number greater than 1 is less than the number.
Let us take any positive number greater than 1, say the number is 2
⇒ [tex]\sqrt{2}=1.414[/tex]
Thus, the statement 1 is true.
Statement 2:
The square root of a positive number is always less than half of the number itself.
Let us take any positive number, say the number is 2
⇒ [tex]\sqrt{2}=1.414[/tex]
Thus, the statement 2 is false.
Statement 3:
The square root of a positive number less than 1 is less than the number.
Let us take any positive number less than 1, say the number is 0.3
⇒ [tex]\sqrt{0.3}=0.5477[/tex]
Thus, the statement 3 is false.
Statement 4:
The square root of a perfect square is not a whole number.
Let us take any perfect square number, say the number is 25
⇒ [tex]\sqrt{25}=5[/tex]
5 is a whole number.
Thus, the statement 4 is false.
Statement 5:
The square root of a positive number less than 1 is between 0 and 1.
Let us take any positive number less than 1, say the number is 0.5
⇒ [tex]\sqrt{0.5} =0.707[/tex]
The square root value is lies between 0 and 1.
Thus, the statement 5 is true.
Hence we can conclude that the statements 1 and 5 are true based on the properties of square root.
Learn more about square roots here
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