If the number under the square root radical has no perfect souare
1 answer:
Answer:
true
Step-by-step explanation:
Examples :
180 = 5 × 2² × 3²
Then
The number 180 has perfect square factors which are 2 and 3
Then
The number √180 can be simplified because:
![\sqrt{180} =\sqrt{5\times 2^{2}\times 3^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B180%7D%20%3D%5Csqrt%7B5%5Ctimes%202%5E%7B2%7D%5Ctimes%203%5E%7B2%7D%7D)
![=\sqrt{5\times \left( 2\times 3\right)^{2} }](https://tex.z-dn.net/?f=%3D%5Csqrt%7B5%5Ctimes%20%5Cleft%28%202%5Ctimes%203%5Cright%29%5E%7B2%7D%20%20%7D)
![=\sqrt{5\times \left( 6\right)^{2} }](https://tex.z-dn.net/?f=%3D%5Csqrt%7B5%5Ctimes%20%5Cleft%28%206%5Cright%29%5E%7B2%7D%20%20%7D)
![=\sqrt{5} \times \sqrt{6^{2}}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B5%7D%20%5Ctimes%20%5Csqrt%7B6%5E%7B2%7D%7D)
![=6\sqrt{5}](https://tex.z-dn.net/?f=%3D6%5Csqrt%7B5%7D)
On the other hand :
10 = 5 × 2
Then
The number 10 has no perfect square factors
Then
The number √10 cannot be simplified because:
![\sqrt{10} =\sqrt{5\times 2} =\sqrt{5} \times \sqrt{2}](https://tex.z-dn.net/?f=%5Csqrt%7B10%7D%20%3D%5Csqrt%7B5%5Ctimes%202%7D%20%3D%5Csqrt%7B5%7D%20%5Ctimes%20%5Csqrt%7B2%7D)
![\text{and} \ \sqrt{5} \times \sqrt{2} \ \text{is not a simplified expression of} \ \sqrt{10} \ \\\text{,in fact it is more complicated than} \ \sqrt{10}](https://tex.z-dn.net/?f=%5Ctext%7Band%7D%20%5C%20%20%5Csqrt%7B5%7D%20%5Ctimes%20%5Csqrt%7B2%7D%20%5C%20%20%5Ctext%7Bis%20not%20a%20simplified%20expression%20of%7D%20%5C%20%20%5Csqrt%7B10%7D%20%5C%20%20%5C%5C%5Ctext%7B%2Cin%20fact%20it%20is%20more%20complicated%20than%7D%20%5C%20%20%5Csqrt%7B10%7D)
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The expression will look like:
6(4m+3a)+m=24m+18a+m=25m+18a
The sentence can be seen completed in the next mak
To figure how many people liked hip hop, you have to multiply 1/5 by 25
1/5 *25 is 5
To figure out how many students liked country, you do
16%*25 which is 4
25-4-5 is 16
So, 16 students like pop music
<span>D. The last two digits of the number are divisible by 4.
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