Can anyone help me work this out
√48 - 2√3 + √20??
Please show the working out
DESPERATE!
√48 - 2√3 + √20 Can anybody help me work this surd out?
2009-02-08 4:55 am
回答 (6)
2009-02-08 5:04 am
✔ 最佳答案
√48 - 2√3 + √20 =√(3*16)-2√3+√(4*5)
=4√3-2√3+2√5
=2√3+2√5 answer
2009-02-08 1:04 pm
â48 - 2â3 + â20
= 4â3 - 2â3 + 2â5
= 2â3 + 2â5
Pretend like a square root phrase (i.e. â3) is a variable, and any coefficient can be combined through adding or subtracting only if the variable is the same. Thus, you must reduce â48 to some form of â3 to combine. After that, there is no way to reduce the problem more. If, however, the equation was + â21 (instead of 20), you could convert that to â7â3 (multiplied), then condense:
= 2â3 + â7â3
= (2 + â7)â3
= 4â3 - 2â3 + 2â5
= 2â3 + 2â5
Pretend like a square root phrase (i.e. â3) is a variable, and any coefficient can be combined through adding or subtracting only if the variable is the same. Thus, you must reduce â48 to some form of â3 to combine. After that, there is no way to reduce the problem more. If, however, the equation was + â21 (instead of 20), you could convert that to â7â3 (multiplied), then condense:
= 2â3 + â7â3
= (2 + â7)â3
2009-02-08 1:01 pm
First we note the prime factorizations of the values under the roots:
48 = 2 * 2 * 2 * 2 * 3 so â48 = 4â3
20 = 2 * 2 * 5 so â20 = 2â5
Now your expression simplifies to
2â3 + 2â5
48 = 2 * 2 * 2 * 2 * 3 so â48 = 4â3
20 = 2 * 2 * 5 so â20 = 2â5
Now your expression simplifies to
2â3 + 2â5
2009-02-08 3:14 pm
â48 - 2â3 + â20
= â(4^2 * 3) - 2â3 + â(2^2 * 5)
= 4â3 - 2â3 + 2â5
= 2â3 + 2â5
= 2(â3 + â5)
= â(4^2 * 3) - 2â3 + â(2^2 * 5)
= 4â3 - 2â3 + 2â5
= 2â3 + 2â5
= 2(â3 + â5)
2009-02-08 1:06 pm
Factoring, we have:
â48|2
24|2
12|2
06|2
03|3
1
â48 = â3 * â2^4 = 2² * â3 = 4â3
â20|2
10|2
05|5
1
â20 = â2² * â5 = 2â5
4â3 - 2â3 + 2â5 = 2â3 + 2â5
â48|2
24|2
12|2
06|2
03|3
1
â48 = â3 * â2^4 = 2² * â3 = 4â3
â20|2
10|2
05|5
1
â20 = â2² * â5 = 2â5
4â3 - 2â3 + 2â5 = 2â3 + 2â5
2009-02-08 1:05 pm
Answer: (2â3) + (2â5)
Work:
48 breaks up into 4 and 12, 20 breaks up into 4 and 5
â4*â12 -2â3+â4*â5
12 breaks up into 3 and 4
=2â4*â3-2â3+2*â5
=4â3-2â3+2â5
=(2â3)+(2â5)
Work:
48 breaks up into 4 and 12, 20 breaks up into 4 and 5
â4*â12 -2â3+â4*â5
12 breaks up into 3 and 4
=2â4*â3-2â3+2*â5
=4â3-2â3+2â5
=(2â3)+(2â5)
收錄日期: 2021-05-01 11:59:30
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