Question

find the square root of the following 7-30√-2​

Answer 1

Answer:

We want to determine the square root of 7−30−2−−−√.

Let a+b−2−−−√=7−30−2−−−√−−−−−−−−−√.

⇒(a+b−2−−−√)2=7−30−2−−−√

⇒a2+2ab−2−−−√−2b2=7−30−2−−−√.

⇒a2−2b2=7 and 2ab=−30.

⇒b=−15a.

⇒a2−450a2=7⇒a4−7a2−450=0.

⇒a2=7±49+1800√2=7±1849√2=7±432

⇒a2=25 or −18.

⇒a=±5 or ±3−2−−−√.

If a=±5, then b=−15a=−15±5=∓3.

If a=±3−2−−−√, then b=−15a=−15±3−2√=−5±−2√=±5−2√2.

⇒a+b−2−−−√=±5∓3−2−−−√, or,

a+b−2−−−√=±3−2−−−√±5−2√2−2−−−√.

⇒a+b−2−−−√=±(5−3−2−−−√).

⇒7−30−2−−−√−−−−−−−−−√=±(5−3−2−−−√).

Step-by-step explanation:

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