When numbers are written in base b, we have 15*22 = 414, the value of b is

• convert the given no. in decimal...
  so..
  (1*b^1+5*b^0)*(2*b^1+2*b^0)=(4*b^2+1*b^1+4*b^0)...
  
  after solving above eq...
  we get.. b = 6 so answer is 6
• 10 years agoHelpfull: Yes(21) No(0)
• another way...
  5*2=10... but we see denominator is 4.... so 10 must have been divided by 6 to give remainder 4 and a carry of 1..then next is 1*2=2 plus 1 from carry..thus it equals to 3. ..thus 15*22=34+X34...add them..answer is 414...thus base is 6...the main thing to feel is...whenever any calculation gets above 6...divide the number by six and write the remainder...it looks tough but once u will feel it...it will be the easiest method
• 10 years agoHelpfull: Yes(2) No(1)
• (414)b => 4*b^2 + 1*b^1 + 4 = 15*22
  now solve..
• 10 years agoHelpfull: Yes(1) No(1)
• b=6.arthematic operations should be done in decimal number system.while converting this into decimal system we will get one quadratic equation by solving b is 6.
• 10 years agoHelpfull: Yes(1) No(0)
• Multiply the last two digits of the LHS digits and equate to the last digit of RHS side
  5*2=4
  10=4
  Ans base = 6
• 8 years agoHelpfull: Yes(1) No(0)
• 6 z corrct
• 10 years agoHelpfull: Yes(0) No(1)
• Let the base be b
  15 in base b means the decimal value is b + 5
  22 in base b means 2b+2
  Similarly, 414 in base b is 4b^2 + b + 4
  Now, the equation is:
  (b+5)(2b+2) = 4b^2 + b + 4
  i.e. 2b^2 + 12b+10 = 4b^2 + b + 4
  i.e. 2b^2 - 11b - 6 = 0
  Solving the quadratic equation: b = 6 or b = -dfrac12
  Now, as the base is an integer, b = 6
• 9 years agoHelpfull: Yes(0) No(0)