Question

find the cube of 9*3​

Answer 1

Answer:

The principal cube root of 9 expressed as a base-3 number is:

2.0020111013

Step-by-step explanation:

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Answer 2

Well, the principal cube root of 9 = 9–√3≈2.08008382393≈2.080083823

Lets express this in base 3.

Remember, with decimal numbers (base 10), units to the right of the decimal point are 10th’s, 100th’s, 1000th’s and so. Note how each column is a tenth of the value of the column to its immediate left. Well, in base 3, the ratios between columns is 3 not 10, giving us columns for 3rd’s, 9th’s, 27th’s, 81st’s and so on.

Let A=2.080083823A=2.080083823

Units digit: This is the integer value of A,A, thus is 2.

Subtract our units digit from AA, giving us 0.0800838230.080083823, then multiply by 3 (our base), giving us 0.2402514690.240251469. Let this be the new value of AA.

3rd’s digit: This is the integer value of A,A, thus is 0.

Subtract our 3rd’s digit from AA, giving us 0.2402514690.240251469, then multiply by 3 (our base), giving us 0.720754410.72075441. Let this be the new value of AA.

9th’s digit: This is the integer value of A,A, thus is 0.

Subtract our 9th’ digit from AA, giving us 0.720754410.72075441, then multiply by 3 (our base), giving us 2.162263222.16226322. Let this be the new value of AA.

27th’s digit: This is the integer value of A,A, thus is 2.

Subtract our 27th’s digit from AA, giving us 0.162263220.16226322, then multiply by 3 (our base), giving us 0.486789670.48678967. Let this be the new value of AA.

81st’s digit: This is the integer value of A,A, thus is 0.

Subtract our 81st’s digit from AA, giving us 0.486789670.48678967, then multiply by 3 (our base), giving us 1.460369001.46036900. Let this be the new value of AA.

243rd’s digit: This is the integer value of AA, thus is 1.

Subtract our 243rd’s digit from AA, giving us 0.460369000.46036900, then multiply by 3 (our base), giving us 1.381107001.38110700. Let this be the new value of AA.

729th’s digit: This is the integer value of AA, thus is 1.

Subtract our 729th’s digit from AA, giving us 0.381107000.38110700, then multiply by 3 (our base), giving us 1.143321011.14332101. Let this be the new value of AA.

2187th’s digit: This is the integer value of AA, thus is 1.

By now, you should have the idea of how to carry on.

The approximate answer (to 9 ‘trinary’ places - I can’t say ‘decimal’ places when I’m not working in base 10) is:

2.002 011 101

Answer: The principal cube root of 9 expressed as a base-3 number is:

2.00201110132.0020111013

When you asked for the cube root, I assumed you wanted the principal cube root. But, just in case, I’ll give you the other roots.

0.59–√3±0.59–√3.3–√i=0.59–√3±0.581−−√6.27−−√6i0.593±0.593.3i=0.593±0.5816.276i

=0.59–√3±0.52187−−−−√6i=0.593±0.521876i

≈1.040041912±3.602810866i≈1.040041912±3.602810866i

where i2=−1i2=−1

Following the same process as used for the principal root, we get:

1.001002012±10.121021110i

I hope it helps you mate and stay safe