Lesson Examples of Radicals

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This Lesson (Examples of Radicals) was created by by Shruti_Mishra(0) About Me : View Source, Show
About Shruti_Mishra: I am a maths graduate from India and am currently persuing masters in Operations Research.
1. 3%2Fsqrt%285%29+=+3%2Asqrt%285%29%2Fsqrt%285%29%5E2+=+%283%2Asqrt%285%29%29%2F5

2. 5x%2F%28sqrt%28x%29-sqrt%28y%29%29+=+%285x%2F%28sqrt%28x%29-sqrt%28y%29%29%29%2A%28%28sqrt%28x%29%2Bsqrt%28y%29%29%2F%28sqrt%28x%29%2Bsqrt%28y%29%29%29+=+5x%2A%28sqrt%28x%29%2Bsqrt%28y%29%29%2F%28x-y%29

3.5%2Asqrt%285%29%2B3%2Asqrt%2845%29+=+5%2Asqrt%285%29%2B3%2Asqrt%289%2A5%29+=+5%2Asqrt%285%29%2B3%2A3%2Asqrt%285%29+=+%285%2B9%29%2Asqrt%285%29+=+14%2Asqrt%285%29

4. 12%2Asqrt%2818%29%2B3%2Asqrt%2850%29%2B6%2Asqrt%2820%29%2B8%2Asqrt%2845%29-6%2Asqrt%28147%29
= 12%2Asqrt%283%5E2%2A2%29%2B3%2Asqrt%285%5E2%2A2%29%2B6%2Asqrt%282%5E2%2A5%29%2B8%2Asqrt%283%5E2%2A5%29-6%2Asqrt%287%5E2%2A3%29
= 12%2A3%2Asqrt%282%29%2B3%2A5%2Asqrt%282%29%2B6%2A2%2Asqrt%285%29%2B8%2A3%2Asqrt%285%29-6%2A7%2Asqrt%283%29
= 36%2Asqrt%282%29%2B15%2Asqrt%282%29%2B12%2Asqrt%285%29%2B24%2Asqrt%285%29-42%2Asqrt%283%29
= 51%2Asqrt%282%29%2B36%2Asqrt%285%29-42%2Asqrt%283%29

5. 3%2Aroot%283%2C5%29+%2A+4%2Aroot%284%2C3%29
The LCM of 3 and 4 is 12.
root%283%2C5%29=root%2812%2C5%5E4%29=root%2812%2C625%29
root%284%2C3%29=root%2812%2C3%5E3%29=root%2812%2C27%29
3%2Aroot%283%2C5%29+%2A+4%2Aroot%284%2C3%29+=+3%2Aroot%2812%2C625%29%2A+4%2Aroot%2812%2C27%29+=+12%2Aroot%2812%2C625%2A27%29+=+12%2Aroot%2812%2C+16875%29

6. %287%2Aroot%283%2C2%29%29%2F%284%2Aroot%285%2C3%29%29
=%287%2Aroot%2815%2C2%5E5%29%29%2F%284%2Aroot%2815%2C3%5E3%29%29
=%287%2Aroot%2815%2C32%29%29%2F%284%2Aroot%2815%2C27%29%29
=%287%2F4%29%2Aroot%2815%2C32%2F27%29

7. Which is greater, sqrt%281%2F3%29 or root%283%2C+1%2F2%29?
Ans. sqrt%281%2F3%29+=+root%286%2C%281%2F3%29%5E3%29+=+root%286%2C1%2F27%29
= root%283%2C1%2F2%29=root%286%2C%281%2F2%29%5E2%29+=+root%286%2C1%2F4%29
Since root%286%2C1%2F4%29+%3E+root%286%2C1%2F27%29, thus root%283%2C+1%2F2%29 is greater than sqrt%281%2F3%29.

8. %28sqrt%283%29%2Bsqrt%282%29%29%2F%28sqrt%283%29-sqrt%282%29%29+=+%28%28sqrt%283%29%2Bsqrt%282%29%29%2F%28sqrt%283%29-sqrt%282%29%29%29%2A%28%28sqrt%283%29%2Bsqrt%282%29%29%2F%28sqrt%283%29%2Bsqrt%282%29%29%29
=%28sqrt%283%29%2Bsqrt%282%29%29%5E2%2F%283-2%29+=+%283%2B2%2Asqrt%283%29%2Asqrt%282%29%2B2%29+=+5%2B2%2Asqrt%286%29

9. 1%2F%28sqrt%283%29-sqrt%282%29-1%29+=+%281%2F%28sqrt%283%29-%28sqrt%282%29%2B1%29%29%29%2A%28%28sqrt%283%29%2B%28sqrt%282%29%2B1%29%29%2F%28sqrt%283%29%2B%28sqrt%282%29%2B1%29%29%29
=%28sqrt%283%29%2B%28sqrt%282%29%2B1%29%29%2F%283-%28sqrt%282%29%2B1%29%5E2%29
=%28sqrt%283%29%2B%28sqrt%282%29%2B1%29%29%2F%283-%282%2B1%2B2%2Asqrt%282%29%29%29
=%28sqrt%283%29%2B%28sqrt%282%29%2B1%29%29%2F%28-2%2Asqrt%282%29%29
=%28-%28sqrt%283%29%2B%28sqrt%282%29%2B1%29%29%2F%282%2Asqrt%282%29%29%29%2A%28sqrt%282%29%2Fsqrt%282%29%29
=%28-%28sqrt%283%29%2Bsqrt%282%29%2B1%29%2Asqrt%282%29%29%2F%284%29
=-%28sqrt%286%29%2B2%2Bsqrt%282%29%29%2F4
=-%28sqrt%286%29%2Bsqrt%282%29%2B2%29%2F4
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